具有不稳定子系统的切换系统稳定性研究
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摘要
摘要切换系统作为最重要的一类混杂系统,常用来模型化各种控制问题及某些自然界的复杂过程.由于存在多个子系统和各种可能切换信号的多样性,导致切换系统虽然表现形式简单,却展现出非常复杂的动力学行为.近几十年来,关于切换系统稳定性的研究一直吸引着众多系统工程师,计算机和数学家们的广泛关注.本文主要以具有不稳定子系统的切换系统为研究对象,这类系统在实际中既具有理论上的挑战性又具有非常重要的应用背景.本文主要内容如下：
第一章主要介绍了本文的研究意义和现状.
第二章研究所有子系统均不稳定的切换线性系统的鲁棒稳定性性质.首先,在特定假设下,给出这类系统能稳的必要条件；其次,利用不变子空间理论及平均驻留时间技术,在给定的两个假设下,分别获得无不确定性和含不确定性的这类系统稳定性的充分条件.切换信号需要满足在两组不稳定子系统之间激活的时间比介于两个常数之间.其中这两个常数可以通过切换系统设计的稳定度计算得来.另外,本章也发展了多Lyapunov函数理论,并给出这种Lyapunov函数构造方法.
第三章研究具有不稳定子系统的离散时间切换线性系统的稳定性问题.首先,给出这类离散切换系统能稳的必要条件；其次,在特定的假设下,利用平均驻留时间技术获得了这类系统稳定的充分条件.最后,给出两个仿真算例演示本章结论有效性.需要指出的是,已经有一些基于平均驻留时间技术研究离散时间切换系统的结论,这些结论多是运用相似于连续情形的手段进行处理.然而,对离散时间切换系统而言,由于系统的状态仅依赖于之前的采样时刻点而不是之前的任意时间点,这导致了可能出现尽管平均驻留时间大于所给出的最小平均驻留时间,切换仍然不能发生或没有意义.为解决这一矛盾,本章提出离散切换信号这一新概念,并对这类离散切换信号发展了平均驻留时间技术.
第四章研究经典Lyapunov函数定理的扩展问题.特别的,本章结论放松了经典Lyapunov函数V需沿系统轨迹非增这一要求.从这一点来说,经典Lyapunov函数可以看做这里的广义Lyapunov函数的一种特例.特别的,非线性系统的稳定性定理可以按如下形式获得：用“V沿系统轨迹容许在某些适当的时间段上增加”替换“V沿系统轨迹非增”.不同于多Lyapunov函数方法,新理论仅需构造一个类Lyapunov函数而不是多个.本章也研究了理论发现在具有不稳定子系统的切换系统中的应用问题.最后两个算例仿真演示结论的有效性.
第五章建立重置正系统与切换正系统的关系.首先,作为重置控制系统的一种扩展,这里提出了重置正系统这一新概念.其次,本章建立起重置正系统与切换正系统之间的某种等价关系.这种关系使我们可以将重置正系统稳定性问题转化为离散时间切换系统稳定性问题,而对于切换系统来说有多种处理方法.然后,借助这种联系,给出在任意重置下重置正系统渐进稳定的充要条件；同时也给出这类系统能稳的充要条件.最后,给出重置正系统的一些稳定判据.
第六章考虑扩展平均驻留时间技术下的离散时间和连续时间切换系统稳定性问题.通过引入三个新的概念,即闭链,r—开链和拟循环切换信号,在这些新切换信号下可以获得平均驻留时间及模型依赖平均驻留时间切换相对应的稳定及能稳性结论.在特定的受限切换信号下,我们发展和丰富了切换系统的已有稳定性结论.另一方面,本章也提出一种获取平均驻留时间及模型依赖平均驻留时间更好下界的方案.
Abstract As one of the most important hybrid systems, switched systems are often used for modeling various control problems and some complex processes in nature. In spite of their apparent simplicity, switched systems display a very complicated dynamical behaviors because of the multiple subsystems and various possible switching signals. In the last decade, the investigations of stability for switched systems have attracted consid-erable attention in Systems Engineering, Computer Sciences and Mathematics commu-nities. This dissertation is devoted to research the switched systems with unstable sub-systems, which is theoretically challenging and of fundamental importance to numerous applications. This paper is organized as follows.
In Chapter1, we introduce some research background and status on the dissertation.
Chapter2studies the problem of robust stability for switched linear systems with all the subsystems being unstable. A necessary condition of stability for switched linear systems is first obtained with certain hypothesis. Then, under two assumptions, suffi-cient conditions of exponential stability for both deterministic and uncertain switched lin-ear systems are presented by using the invariant subspace theory and average dwell time method. Under the given switching signals, the activation time ratio between two sets of unstable subsystems is required to be located between two constants which are computed using the desired stability degree of the switched system. Moreover, we further develop multiple Lyapunov functions and propose a method for constructing multiple Lyapunov functions for the considered switched linear systems with certain switching law.
Chapter3discusses some stability properties of discrete-time switched linear sys-tems (DSLSs) with unstable subsystems. First, under certain hypothesis, the necessary condition of stability for DSLSs is obtained. Second, using the average dwell time (ADT) strategy, we discuss the sufficient condition of exponential stability for switched linear systems with two assumptions. Finally, two examples are presented to show the effec-tiveness of the proposed approach. It is worth pointing out that there are some results for DSLSs obtained by using ADT technique. Those results are based on the switching signal is arbitrary, which usually is used to deal with continuous-time switching law. However, the switching signal of DSLSs is not arbitrar}'because the state of those systems depends only on discrete-time points not on all time points. In order to solve this contradiction, this chapter proposes a novel concept of discrete-time switching signal (DTSS) and develops the ADT technique for DTSS.
In Chapter4, the classical Lyapunov theorems for nonlinear autonomous systems are extended. In particular, our results relax the requirement of V along the system trajec-tories being non-increasing, and thus Lyapunov function is a special case of generalized Lyapunov function. In particular, stability theorems of nonlinear systems are present-ed by replacing "V along the system trajectories is non-increasing" with "V along the system trajectories may increase its value during some proper time intervals". Different from the multiple Lyapunov function method, it only needs to construct a Lyapunov-like function instead of a collection of Lyapunov-like functions. These results are applied to the research for stability of switched systems with unstable subsystems. Two numerical examples are presented to demonstrate the proposed approach.
Chapter5investigates the relationship between reset positive systems and switched positive systems. Firstly, as an extension of reset control systems, a novel concept of reset positive systems (RPS) is proposed. Secondly, the relationship between RPS and switched positive systems (SPS) is established. These relationship provides us an effective approach to transfer the stability of reset control system to investigate the stability of the discrete-time switched system which may be solved with many tools. Thirdly, the sufficient and necessary condition of those RPS asymptotically stable for any reset is obtained, while the sufficient and necessary condition of those RPS stabilizable is also presented. Last but not least, some stability criteria for RPS are given.
Chapter6concerns the problem of stability for switched systems with extended av-erage dwell time in both continuous-time and discrete-time cases. By introducing three novel concepts of closed-chain, r-open-chain and quasi-cyclic switching signals, the sta-bility and stabilization conditions of the switched systems with ADT or mode-dependent ADT (MDADT) switching are obtained, we develops and enriches the existing results of stability under constrained switching. On the other hand, the chapter provides a solution to the open problem of how to obtain a tighter bound on ADT and MDADT.
第一章主要介绍了本文的研究意义和现状.
第二章研究所有子系统均不稳定的切换线性系统的鲁棒稳定性性质.首先,在特定假设下,给出这类系统能稳的必要条件；其次,利用不变子空间理论及平均驻留时间技术,在给定的两个假设下,分别获得无不确定性和含不确定性的这类系统稳定性的充分条件.切换信号需要满足在两组不稳定子系统之间激活的时间比介于两个常数之间.其中这两个常数可以通过切换系统设计的稳定度计算得来.另外,本章也发展了多Lyapunov函数理论,并给出这种Lyapunov函数构造方法.
第三章研究具有不稳定子系统的离散时间切换线性系统的稳定性问题.首先,给出这类离散切换系统能稳的必要条件；其次,在特定的假设下,利用平均驻留时间技术获得了这类系统稳定的充分条件.最后,给出两个仿真算例演示本章结论有效性.需要指出的是,已经有一些基于平均驻留时间技术研究离散时间切换系统的结论,这些结论多是运用相似于连续情形的手段进行处理.然而,对离散时间切换系统而言,由于系统的状态仅依赖于之前的采样时刻点而不是之前的任意时间点,这导致了可能出现尽管平均驻留时间大于所给出的最小平均驻留时间,切换仍然不能发生或没有意义.为解决这一矛盾,本章提出离散切换信号这一新概念,并对这类离散切换信号发展了平均驻留时间技术.
第四章研究经典Lyapunov函数定理的扩展问题.特别的,本章结论放松了经典Lyapunov函数V需沿系统轨迹非增这一要求.从这一点来说,经典Lyapunov函数可以看做这里的广义Lyapunov函数的一种特例.特别的,非线性系统的稳定性定理可以按如下形式获得：用“V沿系统轨迹容许在某些适当的时间段上增加”替换“V沿系统轨迹非增”.不同于多Lyapunov函数方法,新理论仅需构造一个类Lyapunov函数而不是多个.本章也研究了理论发现在具有不稳定子系统的切换系统中的应用问题.最后两个算例仿真演示结论的有效性.
第五章建立重置正系统与切换正系统的关系.首先,作为重置控制系统的一种扩展,这里提出了重置正系统这一新概念.其次,本章建立起重置正系统与切换正系统之间的某种等价关系.这种关系使我们可以将重置正系统稳定性问题转化为离散时间切换系统稳定性问题,而对于切换系统来说有多种处理方法.然后,借助这种联系,给出在任意重置下重置正系统渐进稳定的充要条件；同时也给出这类系统能稳的充要条件.最后,给出重置正系统的一些稳定判据.
第六章考虑扩展平均驻留时间技术下的离散时间和连续时间切换系统稳定性问题.通过引入三个新的概念,即闭链,r—开链和拟循环切换信号,在这些新切换信号下可以获得平均驻留时间及模型依赖平均驻留时间切换相对应的稳定及能稳性结论.在特定的受限切换信号下,我们发展和丰富了切换系统的已有稳定性结论.另一方面,本章也提出一种获取平均驻留时间及模型依赖平均驻留时间更好下界的方案.
Abstract As one of the most important hybrid systems, switched systems are often used for modeling various control problems and some complex processes in nature. In spite of their apparent simplicity, switched systems display a very complicated dynamical behaviors because of the multiple subsystems and various possible switching signals. In the last decade, the investigations of stability for switched systems have attracted consid-erable attention in Systems Engineering, Computer Sciences and Mathematics commu-nities. This dissertation is devoted to research the switched systems with unstable sub-systems, which is theoretically challenging and of fundamental importance to numerous applications. This paper is organized as follows.
In Chapter1, we introduce some research background and status on the dissertation.
Chapter2studies the problem of robust stability for switched linear systems with all the subsystems being unstable. A necessary condition of stability for switched linear systems is first obtained with certain hypothesis. Then, under two assumptions, suffi-cient conditions of exponential stability for both deterministic and uncertain switched lin-ear systems are presented by using the invariant subspace theory and average dwell time method. Under the given switching signals, the activation time ratio between two sets of unstable subsystems is required to be located between two constants which are computed using the desired stability degree of the switched system. Moreover, we further develop multiple Lyapunov functions and propose a method for constructing multiple Lyapunov functions for the considered switched linear systems with certain switching law.
Chapter3discusses some stability properties of discrete-time switched linear sys-tems (DSLSs) with unstable subsystems. First, under certain hypothesis, the necessary condition of stability for DSLSs is obtained. Second, using the average dwell time (ADT) strategy, we discuss the sufficient condition of exponential stability for switched linear systems with two assumptions. Finally, two examples are presented to show the effec-tiveness of the proposed approach. It is worth pointing out that there are some results for DSLSs obtained by using ADT technique. Those results are based on the switching signal is arbitrary, which usually is used to deal with continuous-time switching law. However, the switching signal of DSLSs is not arbitrar}'because the state of those systems depends only on discrete-time points not on all time points. In order to solve this contradiction, this chapter proposes a novel concept of discrete-time switching signal (DTSS) and develops the ADT technique for DTSS.
In Chapter4, the classical Lyapunov theorems for nonlinear autonomous systems are extended. In particular, our results relax the requirement of V along the system trajec-tories being non-increasing, and thus Lyapunov function is a special case of generalized Lyapunov function. In particular, stability theorems of nonlinear systems are present-ed by replacing "V along the system trajectories is non-increasing" with "V along the system trajectories may increase its value during some proper time intervals". Different from the multiple Lyapunov function method, it only needs to construct a Lyapunov-like function instead of a collection of Lyapunov-like functions. These results are applied to the research for stability of switched systems with unstable subsystems. Two numerical examples are presented to demonstrate the proposed approach.
Chapter5investigates the relationship between reset positive systems and switched positive systems. Firstly, as an extension of reset control systems, a novel concept of reset positive systems (RPS) is proposed. Secondly, the relationship between RPS and switched positive systems (SPS) is established. These relationship provides us an effective approach to transfer the stability of reset control system to investigate the stability of the discrete-time switched system which may be solved with many tools. Thirdly, the sufficient and necessary condition of those RPS asymptotically stable for any reset is obtained, while the sufficient and necessary condition of those RPS stabilizable is also presented. Last but not least, some stability criteria for RPS are given.
Chapter6concerns the problem of stability for switched systems with extended av-erage dwell time in both continuous-time and discrete-time cases. By introducing three novel concepts of closed-chain, r-open-chain and quasi-cyclic switching signals, the sta-bility and stabilization conditions of the switched systems with ADT or mode-dependent ADT (MDADT) switching are obtained, we develops and enriches the existing results of stability under constrained switching. On the other hand, the chapter provides a solution to the open problem of how to obtain a tighter bound on ADT and MDADT.
引文
[1]Witsenhausen, H. S., A class of hybrid-state conitnuous-time dynamic systems [J], Automatic Control, IEEE Transactions on,1966,11(6):665-683.
[2]Antsaklis, P. J., Nerode, A., Special issue on hybrid systems [J], Automatic Con-trol, IEEE Transactions on,1998,43(4):455-579.
[3]Morse, A., Pantelides, C., Sastry, S., Schumacher, J., Special issue on hybrid sys-tems [J], Automatica,1999,35(3):347-535.
[4]Evans, R., Savkin, A. V., Special issue on hybrid systems [J], System and Control Letters,1999,38(3):139-207.
[5]Johansen, T. A., Molengraft, R. V., Nijmeijer, H., Special issue on switched sys-tems, piecewise and polytopic linear systems [J], International Journal of Control, 2002,75(16-17):1241-1434.
[6]高军伟,切换系统建模,控制理论与应用研究[D],铁道科学研究院博士学位论文,2003.
[7]Antsaklis, P. J., Stiver, J. A., Lemmon, M., Hybrid system modeling and au-tonomous control systems [M], Springer Berlin Heidelberg,1993:366-392.
[8]Barton, P. I., Lee, C. K., Yunt, M., Optimization of hybrid systems [J], Computers and chemical engineering,2006,30(10):1576-1589.
[9]Branicky, M. S., Universal computation and other capabilities of hybrid and contin-uous dynamical systems [J], Theoretical Computer Science,1995,138(1):67-100.
[10]Liberzon, D., Hybrid feedback stabilization of systems with quantized signals[J], Automatica,2003,39(9):1543-1554.
[11]Liberzon, D., Finite data-rate feedback stabilization of switched and hybrid linear systems[J], Automatica,2013,50(2):409-420.
[12]Sastry, S., Hauser, J., Kokotovic, P., Zero dynamics of regularly perturbed systems may be singularly perturbed [J], Systems and Control Letters,1989,13(4):299-314.
[13]Van Der Schaft, A. J., Schumacher, J. M., An introduction to hybrid dynamical systems [M], London:Springer,2000.
[14]Drescher, D., Bourauel, C., Schumacher, H. A., Frictional forces between bracket and arch wire [J], American Journal of Orthodontics and Dentofacial Orthopedics, 1989,96(5):397-404.
[15]Cai, C., Teel, A. R., Output-to-state stability for hybrid systems [J], Systems and Control Letters,2011,60(1):62-68.
[16]Teel, A. R., Lyapunov conditions certifying stability and recurrence for a class of stochastic hybrid systems [J], Annual Reviews in Control,2013,37(1):1-24.
[17]Liu, X., Shen, J., Stability theory of hybrid dynamical systems with time delay [J], Automatic Control, IEEE Transactions on,2006,51(4):620-625.
[18]Guan, Z. H., Hill, D. J., Shen, X., On hybrid impulsive and switching systems and application to nonlinear control [J], Automatic Control, IEEE Transactions on,2005,50(7):1058-1062.
[19]Guan, Z. H., Hill, D. J., Yao, J., A hybrid impulsive and switching control strategy for synchronization of nonlinear systems and application to Chua's chaotic circuit [J], International Journal of Bifurcation and Chaos,2006,16(01):229-238.
[20]Cheng, D., Guo, L., Lin, Y., et al., Stabilization of switched linear systems [J], IEEE Transactions on Automatic Control,2005,50(5):661-666.
[21]Lemmon, M, D,, He, K. X., Markovsky, I., Supervisory hybrid systems [J], Control Systems, IEEE,1999,19(4):42-55.
[22]Benveniste, A., Le Guernic, P., Hybrid Dynamical Systems theory and nonlinear dynamical systems over finite fields [M], New Trends in Nonlinear Control The-ory. Springer Berlin Heidelberg,1989:483-495.
[23]Peleties, P., DeCarlo, R., Modeling of interacting continuous time and discrete event systems:An example [C], Proceedings of the 26th Annual Allerton Confer-ence on Communication, Control, and Computing.1988:1150-1159.
[24]Branicky, M, S., Universal computation and other capabilities of hybrid and contin-uous dynamical systems [J], Theoretical Computer Science,1995,138(1):67-100.
[25]Zhang, Y, K Mackworth, A., Constraint nets:a semantic model for hybrid dynamic systems [J], Theoretical Computer Science,1995,138(1):211-239.
[26]DeCarlo, R. A., Branicky, M. S., Pettersson, S., et al., Perspectives and results on the stability and stabilizability of hybrid systems [J], Proceedings of the IEEE, 2000,88(7):1069-1082.
[27]史书慧,若干类切换系统的稳定性分析与设计[D],东北大学博士学位论文,2010.
[28]Ooba, T., Funahashi, Y, On a common quadratic Lyapunov function for widely distant systems [J], Automatic Control, IEEE Transactions on,1997,42(12):1697-1699.
[29]Morse, A. S., Supervisory control of families of linear set-point controllers Part I. Exact matching [J], Automatic Control, IEEE Transactions on,1996,41(10): 1413-1431.
[30]Balluchi, A., Di Benedetto, M. D., Pinello, C., et al., Hybrid control in automotive applications:the cut-off control [J], Automatica,1999,35(3):519-535.
[31]Shtessel, Y. B., Raznopolov, O. A., Ozerov, L. A., Control of multiple modular DC-to-DC power converters in conventional and dynamic sliding surfaces [J], Cir-cuits and Systems I:Fundamental Theory and Applications, IEEE Transactions on, 1998,45(10):1091-1100.
[32]Antsaklis, P. J., Koutsoukos, X. D., Hybrid systems:Review and recent progress [J], Software Enabled Control:Information Technology for Dynamical Systems. NY:Wiley-IEEE,2003.
[33]程代展,郭宇骞.切换系统进展[J],控制理论与应用,2005,22(6)：954-960.
[34]Cassandras, C. G., Giua, A., Seatzu, C., et al., DEDS special issue on discrete event methodologies for hybrid systems [J], Discrete Event Dynamic Systems, 2008,18(2):161-162.
[35]任艳频,切换系统的建模、分析与仿真研究[D],清华大学博士学位论文,1999.
[36]Branicky, M. S., Borkar, V. S., Mitter S K. A unified framework for hybrid con-trol [C],11th International Conference on Analysis and Optimization of Systems Discrete Event Systems. Springer Berlin Heidelberg,1994:352-358.
[37]Bemporad, A., Morari, M., Control of systems integrating logic, dynamics, and constraints [J], Automatica,1999,35(3):407-427.
[38]刘皓,线性切换系统有限时间稳定性与控制问题研究[D],哈尔滨工业博士学位论文,2013.
[39]方志明,切换系统稳定性分析与优化控制若干问题研究[D],南京理工大学博士学位论文,2013.
[40]Huang, G. M., Tarn, T. J., Clark, J. W., On the controllability of quantum mechan-ical systems [J], Journal of Mathematical Physics,1983,24(11):2608-2618.
[41]Warren, W. S., Rabitz, H., Dahleh, M.. Coherent control of quantum dynamics:the dream is alive [J], Science,1993,259(12):1581-1585.
[42]Judso, R. S., Rabitz, H., Teachering lasers to control molecules [J], Physical Re-view Letters,1992,68(10):1500-1503.
[43]Doherty, A. C., Jacobs, K., Feedback-control of quantum systems using continuous state estimation [J], Physical review A,1999,60(4):2700-2711.
[44]Rabitz, H., Algorithms for closed loop control of quantum systems [C], IEEE In-ternational conference on decision and control,2000:937-941.
[45]Grivopoulos, S., Bamieh, B., Lyapunov-based control of quantum systems [C], Proceedings of the 42nd IEEE conference on decision and control.2003:434-438.
[46]Mirrahimi, M., Rouchon, P., Turinici, G., Lyapunov control of bilinear Schrodinger equation[J], Automatica,2005,41:1987-1994.
[47]Mirrahimi, M., Lyapunov control of a quantum particle in a decaying potential [J], Annales De 1'institut Henri Poincare-Analyse Nonlineaire,2009,26:1743-1765.
[48]Kuang, S., Cong, S., Lyapunov control methods of closed quantum systems [J], Automatica,2008,34:98-108.
[49]Kuang, S., Cong, S., Population control of equaili,brium states of quantum systems via Lyapunov method [J], Acta Automatica Sinica,2010,36(9):1257-1263.
[50]玉强,吴保卫.双线性Schrodinger方程的Liapunov控制方法[J],陕西师范大学学报：自然科学版,2012,40(6)：6-10.
[51]Liberzon, D., Morse, A. S., Basic problems in stability and design of switched systems [J], Control Systems, IEEE,1999,19(5):59-70.
[52]Bhat, S. P., Beistain, D. S., Nontangency-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria [J], SI AM journal on control and optimization,2003,42(5):1745-1775.
[53]Campbell, S. L., Rose, N. J., Singular perturbation of autonomous linear systems [J], SIAM Journal on Mathematical Analysis,1979,10(3):542-551.
[54]Bhat, S. P., Beistain, D. S., Are-length-based Lyapunov tests for convergence and stability with applications to systems having a continuum of equilibria [J], Math-ematics of Control, Signals, and Systems,2010,22(2):155-184.
[55]Haddad, W. M., Hui, Q., Chellaboina V S. H2 optimal semistable control for linear dynamical systems:An LMI approach [J], Journal of the Franklin Institute,2011, 348(10):2898-2910.
[56]Hui, Q., Haddad, W. M., Bhat, S. P., Finite-time semistability and consensus for nonlinear dynamical networks [J], Automatic Control, IEEE Transactions on, 2008,53(8):1887-1900.
[57]Haddad, W. M., Chellaboina, V. S., Stability and dissipativity theory for nonneg-ative dynamical systems:a unified analysis framework for biological and physi-ological systems [J], Nonlinear Analysis:Real World Applications,2005,6(1): 35-65.
[58]Yu, Q., Wu, B. W., Semistability of nonlinear control systems [J], Advanced Ma-terials Research,2013,748:785-788.
[59]Yu, Q., Wu, B. W., Semistability and weak semistability for nonlinear autonomous systems [J], Mathematica Applicata,2013,26(4):756-764.
[60]Lin, H., Antsaklis, P. J., Stability and stabilizability of switched linear systems:a survey of recent results [J], Automatic control, IEEE Transactions on,2009,54(2): 308-322.
[61]Gurvits, L., Shorten, R., Mason, O., On the stability of switched positive linear systems [J], Automatic Control, IEEE Transactions on,2007,52(6):1099-1103.
[62]Zhao, X., Zhang, L., Shi, P., et al., Stability of switched positive linear systems with average dwell time switching [J], Automatica,2012,48(6):1132-1137.
[63]Ding, X., Shu, L., Wang, Z., On stability for switched linear positive systems [J], Mathematical and Computer Modelling,2011,53(5):1044-1055.
[64]Zhai, G., Hu, B., Yasuda, K., et al., Stability analysis of switched systems with stable and unstable subsystems:an average dwell time approach [J], International Journal of Systems Science,2001,32(8):1055-1061.
[65]Margaliot, M., Stability analysis of switched systems using variational principles: An introduction [J], Automatica,2006,42(12):2059-2077.
[66]Feng, L., Song, Y. D., Stability condition for sampled data based control of linear continuous switched systems [J], Systems and Control Letters,2011,60(10):787-797.
[67]Wang, C. H., Zhang, L. X., Gao, H. J., et al., Delay-dependent stability and sta-bilization of a class of linear switched time-varying delay systems [C], Machine Learning and Cybernetics,2005. Proceedings of 2005 International Conference on. IEEE,2005,2:917-922.
[68]Hui, Q., Lyapunov-based semistability analysis for discrete-time switched network systems [C], American Control Conference (ACC), IEEE,2011:2602-2606.
[69]Hui, Q., Haddad, W. M., Semistability of switched dynamical systems, Part I:Lin-ear system theory [J], Nonlinear Analysis:Hybrid Systems,2009,3(3):343-353.
[70]Hui, Q., Haddad, W. M., Semistability of switched dynamical systems, Part II: Non-linear system theory [J], Nonlinear Analysis:Hybrid Systems,2009,3(3): 354-362.
[71]Hale, J. LaSlle, J. P., Differential equations and dynamical systems [M], Academic Press,New York,1967.
[72]Cheng, D., Wang, J., Hu, X., An extension of LaSalle's invariance principle and its application to multi-agent consensus [J], Automatic Control, IEEE Transactions on,2008,53(7):1765-1770.
[73]Wang, J. H., Cheng, D. Z., Stability of switched nonlinear systems via extension-s of LaSalle's invariance principle [J], Science in China Series F:Information Sciences,2009,52(1):84-90.
[74]Mancilla-Aguilar, J. L., Garcia, R. A., An extension of LaSalle's invariance prin-ciple for switched systems [J], Systems and Control Letters,2006,55(5):376-384.
[75]Michele, C., Valentino, M. C., Oliveira, V. A., et al., An extension of the invari-ance principle for dwell-time switched nonlinear systems [J], Systems and Control Letters,2012,61(4):580-586.
[76]Wang, J., Cheng, D., Hu, X., An extension of LaSalle's invariance principle for a class of switched linear systems [J], Systems and Control Letters,2009,58(10): 754-758.
[77]Hespanha, J. P., Uniform stability of switched linear systems:extensions of LaSalle's invariance principle [J], Automatic Control, IEEE Transactions on,2004, 49(4):470-482.
[78]Hespanha, J. P., Liberzon, D., Sontag, E. D., Nonlinear Observability and an In-variance Principle for Switched Systems (I) [C], IEEE Conference on Decision and Control. IEEE; 2002,4:4300-4305.
[79]Bacciotti, A., Mazzi, L., An invariance principle for nonlinear switched systems [J], Systems and Control Letters,2005,54(11):1109-1119.
[80]Chellaboina, V. S., Leonessa, A., Haddad, W. M., Generalized Lyapunov and In-variant Set Theorems for Nonlinear Dynamical Systems [J], Systems and Control Letters,1999,38(4/5):289-295.
[81]Valentino, M. C, Oliveira, V. A., Alberto, L. F., Sant' Anna, D. A., An Exten-sion of the Invariance Principle for Dwell-time Switched Systems [J], Systems and Control Letters,2012,61(4):580-586.
[82]Khalil, H. K., Nonlinear Systems [M], Upper Saddle River:Prentice hall,2002.
[83]Sastry, S., Nonlinear Systems:Analysis, Stability, and Control [M], New York: Springer-Verlag,1999.
[84]Chellaboina, V. S., Bhat, S. P., Haddad, W. M., An Invariance Principle for Non-linear Hybrid and Impulsive Dynamical Systems [J], Nonlinear Analysis,2003, 53(3/4):527-550.
[85]Orlov, Y., Finite time stability and robust control synthesis of uncertain switched systems [J], SIAM Journal on Control and Optimization,2004,43(4):1253-1271.
[86]Bhat, S. P., Bernstein, D.S., Finite-time stability of continuous autonomous sys-tems [J], SIAM Journal on Control and Optimization,2000,38(3):751-766.
[87]Sheng, W., Zhang, X., Finite-time stability of switched systems [C], Control and Decision Conference (CCDC),2012 24th Chinese. IEEE,2012:270-274.
[88]Vu, L., Chatterjee, D., Liberzon, D., Input-to-state stability of switched systems and switching adaptive control [J], Automatica,2007,43(4):639-646.
[89]Sontag, E. D., Input to state stability:Basic concepts and results [M], Nonlinear and optimal control theory. Springer Berlin Heidelberg,2008:163-220.
[90]Wang, Y. E., Sun, X. M., Shi, P., et al., Stabilization of a class of switched linear neutral systems under asynchronous switching [J], IEEE Transactions on Auto-matic Control,2013,58(8):2114-2119.
[91]Wang, Y. E., Sun, X. M., Shi, P., et al., Input-to-state stability of switched nonlinear systems with time delays under asynchronous switching [J], IEEE Transactions on Cybernetics,2013,43(6):2261-2265.
[92]Liu, J., Liu, X., Xie, W. C., Input-to-state stability of impulsive and switching hybrid systems with time-delay [J], Automatica,2011,47(5):899-908.
[93]Guckenheimer, J., Holmes, P., Nonlinear oscillations, dynamical systems, and bi-furcations of vector fields [M], Springer Verlag:New York,1983.
[94]Zhai, G., Lin, H., Antsaklis, P. J., Quadratic stabilizability of switched linear sys-tems with polytopic uncertainties [J], International Journal of Control,2003,76(7): 747-753.
[95]Balde, M., Boscain, U., Mason, P., A note on stability conditions for planar switched systems [J], International journal of control,2009,82(10):1882-1888.
[96]Zhu, W., Stability analysis of switched impulsive systems with time delays [J], Nonlinear Analysis:Hybrid Systems,2010,4(3):608-617.
[97]Ma, S., Zhang, C., Wu, Z., Delay-dependent stability and H∞, control for uncertain discrete switched singular systems with time-delay [J], Applied Mathematics and Computation,2008,206(1):413-424.
[98]Shi, S., Zhang, Q., Yuan, Z., et al., Hybrid impulsive control for switched singular systems [J], IET control theory and applications,2011,5(1):103-111.
[99]Lin, J. X., Fei, S. M., Robust exponential admissibility of uncertain switched sin-gular time-delay systems [J], Acta Automatica Sinica,2010,36(12):1773-1779.
[100]Yao, J., Guan, Z. H., Chen, G., et al., Stability, robust stabilization and H∞ con-trol of singular-impulsive systems via switching control [J], Systems and Control Letters,2006,55(11):879-886.
[101]Zhao, J., Hill, D. J., Dissipativity theory for switched systems [J], Automatic Con-trol, IEEE Transactions on,2008,53(4):941-953.
[102]Zhao, J., Hill, D. J., Passivity and stability of switched systems:a multiple storage function method [J], Systems and Control Letters,2008,57(2):158-164.
[103]Zhao, J., Hill, D. J., A notion of passivity for switched systems with state-dependent switching [J], Journal of Control Theory and Applications,2006,4(1): 70-75.
[104]Zhang, L., Gao, H., Asynchronously switched control of switched linear systems with average dwell time [J], Automatica,2010,46(5):953-958.
[105]Zhang, L., Shi, P., Stability, L2-gain and asynchronous control of discrete-time switched systems with average dwell time [J], Automatic Control, IEEE Transac-tions on,2009,54(9):2192-2199.
[106]Wang, Y. E., Sun, X. M., Zhao, J., Asynchronous H∞ control of switched delay sys-tems with average dwell time [J], Journal of the Franklin Institute,2012,349(10): 3159-3169.
[107]Zhao, X., Shi, P., Zhang, L., Asynchronously switched control of a class of slowly switched linear systems [J], Systems and Control Letters,2012,61 (12):1151-1156.
[108]Xie, D., Wang, L., Hao, F., et al., Robust stability analysis and control synthe-sis for discrete-time uncertain switched systems [C], Decision and Control,2003. Proceedings.42nd IEEE Conference on. IEEE,2003,5:4812-4817.
[109]Lin, J., Fei, S., Wu, Q., Reliable H∞ filtering for discrete-time switched singu-lar systems with time-varying delay [J], Circuits, Systems, and Signal Processing, 2012,31(3):1191-1214.
[110]Du, D., Zhou, S., Zhang, B., Generalized H2 output feedback controller design for uncertain discrete-time switched systems via switched Lyapunov functions [J], Nonlinear Analysis:Theory, Methods and Applications,2006,65(11):2135-2146.
[111]Liberzon, D., Switching in systems and control [M], Springer,2003.
[112]Duarte-Mermoud M A, Ordonez-Hurtado R H, Zagalak P. A method for deter-mining the non-existence of a common quadratic Lyapunov function for switched linear systems based on particle swarm optimisation [J], International Journal of Systems Science,2012,43(11):2015-2029.
[113]Sun, X. M., Wang, W, Integral input-to-state stability for hybrid delayed systems with unstable continuous dynamics [J], Automatica,2012,48(9):2359-2364.
[114]Sun, X. M., Liu, G. P., Wang, W., et al., Stability analysis for systems with large delay period:a switching method [J], International Journal of Innovative Comput-ing, Information and Control,2012,8(6):4235-4247.
[115]Niu, B., Zhao, J., Tracking control for output-constrained nonlinear switched sys-tems with a barrier Lyapunov function [J], International Journal of Systems Sci-ence,2013,44(5):978-985.
[116]Wang, Y., Shi, X., Zuo, Z., et al., On finite-time stability for nonlinear impulsive switched systems [J], Nonlinear Analysis:Real World Applications,2013,14(1): 807-814.
[117]Wicks, M., Peleties, P., DeCarlo, R., Switched controller synthesis for the quadratic stabilisation of a pair of unstable linear systems [J], European Journal of Control, 1998,4(2):140-147.
[118]Lien, C. H., Yu, K. W., Chung, Y. J., et al., Switching signal design for global exponential stability of uncertain switched nonlinear systems with time-varying delay [J], Nonlinear Analysis:Hybrid Systems,2011,5(1):10-19.
[119]Phat, V. N., Botmart, T., Niamsup, P., Switching design for exponential stability of a class of nonlinear hybrid time-delay systems [J], Nonlinear Analysis:Hybrid Systems,2009,3(1):1-10.
[120]Sun, X. M., Wang, W., Liu, G. P., et al., Stability analysis for linear switched systems with time-varying delay [J], Systems, Man, and Cybernetics, Part B:Cy-bernetics, IEEE Transactions on,2008,38(2):528-533.
[121]Polderman, J. W., Langerak, R., Stability and robustness of planar switching linear systems [J], Systems and Control Letters,2012,61(9):904-910.
[122]Li, T. F., Dimiro vski, G. M., Liu, Y., et al., Improved stability of a class of switched neutral systems via Lyapunov-Krasovskii functionals and an average dwell-time scheme [J], International Journal of systems science,2013,44(6):1076-1088.
[123]Guckenheimer, J., Holmes, P., Nonlinear oscillations, dynamical systems, and bi-furcations of vector fields [M], Springer Verlag:New York,1983.
[124]Horn, R. A., Johnson, C. R., Matrix analysis [M], Cambridge university press, 2012.
[125]Bhatia, R., Matrix analysis [M], Springer,1997.
[126]Zhao, X., Zhang, L., Shi, P., et al., Stability and stabilization of switched linear systems with mode-dependent average dwell time [J], Automatic Control, IEEE Transactions on,2012,57(7):1809-1815.
[127]Zhang, J., Han, Z., Zhu, F., et al., Stability and stabilization of positive switched systems with mode-dependent average dwell time [J], Nonlinear Analysis:Hybrid Systems,2013,9:42-55.
[128]Yu, Q., Wu, B., Robust stability analysis of uncertain switched linear systems with unstable subsystems [J], International Journal of Systems Science,2013 (ahead-of-print):1-10.
[129]Hernandez-Vargas, E., Colaneri, P., Middleton, R., et al., Discrete□time control for switched positive systems with application to mitigating viral escape [J], Inter-national Journal of Robust and Nonlinear Control,2011,21(10):1093-1111.
[130]Du, D., Jiang, B., Shi, P., et al., Hoo filtering of discrete-time switched systems with state delays via switched Lyapunov function approach [J], Automatic Control, IEEE Transactions on,2007,52(8):1520-1525.
[131]Geromel, J. C., Colaneri, P., Stability and stabilization of discrete time switched systems [J], International Journal of Control,2006,79(7):719-728.
[132]Sun, Y. G., Wang, L., Xie, G., Delay-dependent robust stability and stabilization for discrete-time switched systems with mode-dependent time-varying delays [J], Applied Mathematics and Computation,2006,180(2):428-435.
[133]Lyapunov, A. M., The general problem of the stability of motion [J], International Journal of Control,1992,55(3):531-534.
[134]Passino, K. M., Michel, A. N., Antsaklis, P. J., Lyapunov stability of a class of discrete event systems [J], Automatic Control, IEEE Transactions on,1994,39(2): 269-279.
[135]Upadhyay, R. K., Iyengar, S. R. K., Rai, V., Stability and complexity in ecological systems [J], Chaos, Solitons and Fractals,2000,11(4):533-542.
[136]Wang, Y, Shi, X., Zuo, Z., et al. On finite-time stability for nonlinear impulsive switched systems [J], Nonlinear Analysis:Real World Applications,2013,14(1): 807-814.
[137]Sun, X. M., Wang, W, Integral input-to-state stability for hybrid delayed systems with unstable continuous dynamics [J], Automatica,2012,48(9):2359-2364.
[138]Aleksandrov, A. Y, Kosov, A. A., Platonov, A. V., On the asymptotic stability of switched homogeneous systems [J], Systems and Control Letters,2012,61(1): 127-133.
[139]Clegg, J. C., A nonlinear integrator for servomechanisms [J], American Institute of Electrical Engineers, Part II:Applications and Industry, Transactions of the,1958, 77(1):41-42.
[140]Banos, A., Barreiro, A., Stability of Reset Control Systems [M], Reset Control Systems. Springer London,2012:93-145.
[141]Nesic, D., Zaccarian, L., Teel, A. R., Stability properties of reset systems [J], Au-tomatica,2008,44(8):2019-2026.
[142]Banos, A., Carrasco, J., Barreiro, A., Reset times-dependent stability of reset con-trol with unstable base systems[C], Industrial Electronics,2007. ISIE 2007. IEEE International Symposium on. IEEE,2007:163-168.
[143]Guo, Y, Gui, W., Yang, C., et al., Stability analysis and design of reset control systems with discrete-time triggering conditions [J], Automatica,2012,48(3):528-535.
[144]玉强,吴保卫.一类正线性系统的整体性质[J],云南大学学报：自然科学版,2014,36(1)：6-11.
[2]Antsaklis, P. J., Nerode, A., Special issue on hybrid systems [J], Automatic Con-trol, IEEE Transactions on,1998,43(4):455-579.
[3]Morse, A., Pantelides, C., Sastry, S., Schumacher, J., Special issue on hybrid sys-tems [J], Automatica,1999,35(3):347-535.
[4]Evans, R., Savkin, A. V., Special issue on hybrid systems [J], System and Control Letters,1999,38(3):139-207.
[5]Johansen, T. A., Molengraft, R. V., Nijmeijer, H., Special issue on switched sys-tems, piecewise and polytopic linear systems [J], International Journal of Control, 2002,75(16-17):1241-1434.
[6]高军伟,切换系统建模,控制理论与应用研究[D],铁道科学研究院博士学位论文,2003.
[7]Antsaklis, P. J., Stiver, J. A., Lemmon, M., Hybrid system modeling and au-tonomous control systems [M], Springer Berlin Heidelberg,1993:366-392.
[8]Barton, P. I., Lee, C. K., Yunt, M., Optimization of hybrid systems [J], Computers and chemical engineering,2006,30(10):1576-1589.
[9]Branicky, M. S., Universal computation and other capabilities of hybrid and contin-uous dynamical systems [J], Theoretical Computer Science,1995,138(1):67-100.
[10]Liberzon, D., Hybrid feedback stabilization of systems with quantized signals[J], Automatica,2003,39(9):1543-1554.
[11]Liberzon, D., Finite data-rate feedback stabilization of switched and hybrid linear systems[J], Automatica,2013,50(2):409-420.
[12]Sastry, S., Hauser, J., Kokotovic, P., Zero dynamics of regularly perturbed systems may be singularly perturbed [J], Systems and Control Letters,1989,13(4):299-314.
[13]Van Der Schaft, A. J., Schumacher, J. M., An introduction to hybrid dynamical systems [M], London:Springer,2000.
[14]Drescher, D., Bourauel, C., Schumacher, H. A., Frictional forces between bracket and arch wire [J], American Journal of Orthodontics and Dentofacial Orthopedics, 1989,96(5):397-404.
[15]Cai, C., Teel, A. R., Output-to-state stability for hybrid systems [J], Systems and Control Letters,2011,60(1):62-68.
[16]Teel, A. R., Lyapunov conditions certifying stability and recurrence for a class of stochastic hybrid systems [J], Annual Reviews in Control,2013,37(1):1-24.
[17]Liu, X., Shen, J., Stability theory of hybrid dynamical systems with time delay [J], Automatic Control, IEEE Transactions on,2006,51(4):620-625.
[18]Guan, Z. H., Hill, D. J., Shen, X., On hybrid impulsive and switching systems and application to nonlinear control [J], Automatic Control, IEEE Transactions on,2005,50(7):1058-1062.
[19]Guan, Z. H., Hill, D. J., Yao, J., A hybrid impulsive and switching control strategy for synchronization of nonlinear systems and application to Chua's chaotic circuit [J], International Journal of Bifurcation and Chaos,2006,16(01):229-238.
[20]Cheng, D., Guo, L., Lin, Y., et al., Stabilization of switched linear systems [J], IEEE Transactions on Automatic Control,2005,50(5):661-666.
[21]Lemmon, M, D,, He, K. X., Markovsky, I., Supervisory hybrid systems [J], Control Systems, IEEE,1999,19(4):42-55.
[22]Benveniste, A., Le Guernic, P., Hybrid Dynamical Systems theory and nonlinear dynamical systems over finite fields [M], New Trends in Nonlinear Control The-ory. Springer Berlin Heidelberg,1989:483-495.
[23]Peleties, P., DeCarlo, R., Modeling of interacting continuous time and discrete event systems:An example [C], Proceedings of the 26th Annual Allerton Confer-ence on Communication, Control, and Computing.1988:1150-1159.
[24]Branicky, M, S., Universal computation and other capabilities of hybrid and contin-uous dynamical systems [J], Theoretical Computer Science,1995,138(1):67-100.
[25]Zhang, Y, K Mackworth, A., Constraint nets:a semantic model for hybrid dynamic systems [J], Theoretical Computer Science,1995,138(1):211-239.
[26]DeCarlo, R. A., Branicky, M. S., Pettersson, S., et al., Perspectives and results on the stability and stabilizability of hybrid systems [J], Proceedings of the IEEE, 2000,88(7):1069-1082.
[27]史书慧,若干类切换系统的稳定性分析与设计[D],东北大学博士学位论文,2010.
[28]Ooba, T., Funahashi, Y, On a common quadratic Lyapunov function for widely distant systems [J], Automatic Control, IEEE Transactions on,1997,42(12):1697-1699.
[29]Morse, A. S., Supervisory control of families of linear set-point controllers Part I. Exact matching [J], Automatic Control, IEEE Transactions on,1996,41(10): 1413-1431.
[30]Balluchi, A., Di Benedetto, M. D., Pinello, C., et al., Hybrid control in automotive applications:the cut-off control [J], Automatica,1999,35(3):519-535.
[31]Shtessel, Y. B., Raznopolov, O. A., Ozerov, L. A., Control of multiple modular DC-to-DC power converters in conventional and dynamic sliding surfaces [J], Cir-cuits and Systems I:Fundamental Theory and Applications, IEEE Transactions on, 1998,45(10):1091-1100.
[32]Antsaklis, P. J., Koutsoukos, X. D., Hybrid systems:Review and recent progress [J], Software Enabled Control:Information Technology for Dynamical Systems. NY:Wiley-IEEE,2003.
[33]程代展,郭宇骞.切换系统进展[J],控制理论与应用,2005,22(6)：954-960.
[34]Cassandras, C. G., Giua, A., Seatzu, C., et al., DEDS special issue on discrete event methodologies for hybrid systems [J], Discrete Event Dynamic Systems, 2008,18(2):161-162.
[35]任艳频,切换系统的建模、分析与仿真研究[D],清华大学博士学位论文,1999.
[36]Branicky, M. S., Borkar, V. S., Mitter S K. A unified framework for hybrid con-trol [C],11th International Conference on Analysis and Optimization of Systems Discrete Event Systems. Springer Berlin Heidelberg,1994:352-358.
[37]Bemporad, A., Morari, M., Control of systems integrating logic, dynamics, and constraints [J], Automatica,1999,35(3):407-427.
[38]刘皓,线性切换系统有限时间稳定性与控制问题研究[D],哈尔滨工业博士学位论文,2013.
[39]方志明,切换系统稳定性分析与优化控制若干问题研究[D],南京理工大学博士学位论文,2013.
[40]Huang, G. M., Tarn, T. J., Clark, J. W., On the controllability of quantum mechan-ical systems [J], Journal of Mathematical Physics,1983,24(11):2608-2618.
[41]Warren, W. S., Rabitz, H., Dahleh, M.. Coherent control of quantum dynamics:the dream is alive [J], Science,1993,259(12):1581-1585.
[42]Judso, R. S., Rabitz, H., Teachering lasers to control molecules [J], Physical Re-view Letters,1992,68(10):1500-1503.
[43]Doherty, A. C., Jacobs, K., Feedback-control of quantum systems using continuous state estimation [J], Physical review A,1999,60(4):2700-2711.
[44]Rabitz, H., Algorithms for closed loop control of quantum systems [C], IEEE In-ternational conference on decision and control,2000:937-941.
[45]Grivopoulos, S., Bamieh, B., Lyapunov-based control of quantum systems [C], Proceedings of the 42nd IEEE conference on decision and control.2003:434-438.
[46]Mirrahimi, M., Rouchon, P., Turinici, G., Lyapunov control of bilinear Schrodinger equation[J], Automatica,2005,41:1987-1994.
[47]Mirrahimi, M., Lyapunov control of a quantum particle in a decaying potential [J], Annales De 1'institut Henri Poincare-Analyse Nonlineaire,2009,26:1743-1765.
[48]Kuang, S., Cong, S., Lyapunov control methods of closed quantum systems [J], Automatica,2008,34:98-108.
[49]Kuang, S., Cong, S., Population control of equaili,brium states of quantum systems via Lyapunov method [J], Acta Automatica Sinica,2010,36(9):1257-1263.
[50]玉强,吴保卫.双线性Schrodinger方程的Liapunov控制方法[J],陕西师范大学学报：自然科学版,2012,40(6)：6-10.
[51]Liberzon, D., Morse, A. S., Basic problems in stability and design of switched systems [J], Control Systems, IEEE,1999,19(5):59-70.
[52]Bhat, S. P., Beistain, D. S., Nontangency-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria [J], SI AM journal on control and optimization,2003,42(5):1745-1775.
[53]Campbell, S. L., Rose, N. J., Singular perturbation of autonomous linear systems [J], SIAM Journal on Mathematical Analysis,1979,10(3):542-551.
[54]Bhat, S. P., Beistain, D. S., Are-length-based Lyapunov tests for convergence and stability with applications to systems having a continuum of equilibria [J], Math-ematics of Control, Signals, and Systems,2010,22(2):155-184.
[55]Haddad, W. M., Hui, Q., Chellaboina V S. H2 optimal semistable control for linear dynamical systems:An LMI approach [J], Journal of the Franklin Institute,2011, 348(10):2898-2910.
[56]Hui, Q., Haddad, W. M., Bhat, S. P., Finite-time semistability and consensus for nonlinear dynamical networks [J], Automatic Control, IEEE Transactions on, 2008,53(8):1887-1900.
[57]Haddad, W. M., Chellaboina, V. S., Stability and dissipativity theory for nonneg-ative dynamical systems:a unified analysis framework for biological and physi-ological systems [J], Nonlinear Analysis:Real World Applications,2005,6(1): 35-65.
[58]Yu, Q., Wu, B. W., Semistability of nonlinear control systems [J], Advanced Ma-terials Research,2013,748:785-788.
[59]Yu, Q., Wu, B. W., Semistability and weak semistability for nonlinear autonomous systems [J], Mathematica Applicata,2013,26(4):756-764.
[60]Lin, H., Antsaklis, P. J., Stability and stabilizability of switched linear systems:a survey of recent results [J], Automatic control, IEEE Transactions on,2009,54(2): 308-322.
[61]Gurvits, L., Shorten, R., Mason, O., On the stability of switched positive linear systems [J], Automatic Control, IEEE Transactions on,2007,52(6):1099-1103.
[62]Zhao, X., Zhang, L., Shi, P., et al., Stability of switched positive linear systems with average dwell time switching [J], Automatica,2012,48(6):1132-1137.
[63]Ding, X., Shu, L., Wang, Z., On stability for switched linear positive systems [J], Mathematical and Computer Modelling,2011,53(5):1044-1055.
[64]Zhai, G., Hu, B., Yasuda, K., et al., Stability analysis of switched systems with stable and unstable subsystems:an average dwell time approach [J], International Journal of Systems Science,2001,32(8):1055-1061.
[65]Margaliot, M., Stability analysis of switched systems using variational principles: An introduction [J], Automatica,2006,42(12):2059-2077.
[66]Feng, L., Song, Y. D., Stability condition for sampled data based control of linear continuous switched systems [J], Systems and Control Letters,2011,60(10):787-797.
[67]Wang, C. H., Zhang, L. X., Gao, H. J., et al., Delay-dependent stability and sta-bilization of a class of linear switched time-varying delay systems [C], Machine Learning and Cybernetics,2005. Proceedings of 2005 International Conference on. IEEE,2005,2:917-922.
[68]Hui, Q., Lyapunov-based semistability analysis for discrete-time switched network systems [C], American Control Conference (ACC), IEEE,2011:2602-2606.
[69]Hui, Q., Haddad, W. M., Semistability of switched dynamical systems, Part I:Lin-ear system theory [J], Nonlinear Analysis:Hybrid Systems,2009,3(3):343-353.
[70]Hui, Q., Haddad, W. M., Semistability of switched dynamical systems, Part II: Non-linear system theory [J], Nonlinear Analysis:Hybrid Systems,2009,3(3): 354-362.
[71]Hale, J. LaSlle, J. P., Differential equations and dynamical systems [M], Academic Press,New York,1967.
[72]Cheng, D., Wang, J., Hu, X., An extension of LaSalle's invariance principle and its application to multi-agent consensus [J], Automatic Control, IEEE Transactions on,2008,53(7):1765-1770.
[73]Wang, J. H., Cheng, D. Z., Stability of switched nonlinear systems via extension-s of LaSalle's invariance principle [J], Science in China Series F:Information Sciences,2009,52(1):84-90.
[74]Mancilla-Aguilar, J. L., Garcia, R. A., An extension of LaSalle's invariance prin-ciple for switched systems [J], Systems and Control Letters,2006,55(5):376-384.
[75]Michele, C., Valentino, M. C., Oliveira, V. A., et al., An extension of the invari-ance principle for dwell-time switched nonlinear systems [J], Systems and Control Letters,2012,61(4):580-586.
[76]Wang, J., Cheng, D., Hu, X., An extension of LaSalle's invariance principle for a class of switched linear systems [J], Systems and Control Letters,2009,58(10): 754-758.
[77]Hespanha, J. P., Uniform stability of switched linear systems:extensions of LaSalle's invariance principle [J], Automatic Control, IEEE Transactions on,2004, 49(4):470-482.
[78]Hespanha, J. P., Liberzon, D., Sontag, E. D., Nonlinear Observability and an In-variance Principle for Switched Systems (I) [C], IEEE Conference on Decision and Control. IEEE; 2002,4:4300-4305.
[79]Bacciotti, A., Mazzi, L., An invariance principle for nonlinear switched systems [J], Systems and Control Letters,2005,54(11):1109-1119.
[80]Chellaboina, V. S., Leonessa, A., Haddad, W. M., Generalized Lyapunov and In-variant Set Theorems for Nonlinear Dynamical Systems [J], Systems and Control Letters,1999,38(4/5):289-295.
[81]Valentino, M. C, Oliveira, V. A., Alberto, L. F., Sant' Anna, D. A., An Exten-sion of the Invariance Principle for Dwell-time Switched Systems [J], Systems and Control Letters,2012,61(4):580-586.
[82]Khalil, H. K., Nonlinear Systems [M], Upper Saddle River:Prentice hall,2002.
[83]Sastry, S., Nonlinear Systems:Analysis, Stability, and Control [M], New York: Springer-Verlag,1999.
[84]Chellaboina, V. S., Bhat, S. P., Haddad, W. M., An Invariance Principle for Non-linear Hybrid and Impulsive Dynamical Systems [J], Nonlinear Analysis,2003, 53(3/4):527-550.
[85]Orlov, Y., Finite time stability and robust control synthesis of uncertain switched systems [J], SIAM Journal on Control and Optimization,2004,43(4):1253-1271.
[86]Bhat, S. P., Bernstein, D.S., Finite-time stability of continuous autonomous sys-tems [J], SIAM Journal on Control and Optimization,2000,38(3):751-766.
[87]Sheng, W., Zhang, X., Finite-time stability of switched systems [C], Control and Decision Conference (CCDC),2012 24th Chinese. IEEE,2012:270-274.
[88]Vu, L., Chatterjee, D., Liberzon, D., Input-to-state stability of switched systems and switching adaptive control [J], Automatica,2007,43(4):639-646.
[89]Sontag, E. D., Input to state stability:Basic concepts and results [M], Nonlinear and optimal control theory. Springer Berlin Heidelberg,2008:163-220.
[90]Wang, Y. E., Sun, X. M., Shi, P., et al., Stabilization of a class of switched linear neutral systems under asynchronous switching [J], IEEE Transactions on Auto-matic Control,2013,58(8):2114-2119.
[91]Wang, Y. E., Sun, X. M., Shi, P., et al., Input-to-state stability of switched nonlinear systems with time delays under asynchronous switching [J], IEEE Transactions on Cybernetics,2013,43(6):2261-2265.
[92]Liu, J., Liu, X., Xie, W. C., Input-to-state stability of impulsive and switching hybrid systems with time-delay [J], Automatica,2011,47(5):899-908.
[93]Guckenheimer, J., Holmes, P., Nonlinear oscillations, dynamical systems, and bi-furcations of vector fields [M], Springer Verlag:New York,1983.
[94]Zhai, G., Lin, H., Antsaklis, P. J., Quadratic stabilizability of switched linear sys-tems with polytopic uncertainties [J], International Journal of Control,2003,76(7): 747-753.
[95]Balde, M., Boscain, U., Mason, P., A note on stability conditions for planar switched systems [J], International journal of control,2009,82(10):1882-1888.
[96]Zhu, W., Stability analysis of switched impulsive systems with time delays [J], Nonlinear Analysis:Hybrid Systems,2010,4(3):608-617.
[97]Ma, S., Zhang, C., Wu, Z., Delay-dependent stability and H∞, control for uncertain discrete switched singular systems with time-delay [J], Applied Mathematics and Computation,2008,206(1):413-424.
[98]Shi, S., Zhang, Q., Yuan, Z., et al., Hybrid impulsive control for switched singular systems [J], IET control theory and applications,2011,5(1):103-111.
[99]Lin, J. X., Fei, S. M., Robust exponential admissibility of uncertain switched sin-gular time-delay systems [J], Acta Automatica Sinica,2010,36(12):1773-1779.
[100]Yao, J., Guan, Z. H., Chen, G., et al., Stability, robust stabilization and H∞ con-trol of singular-impulsive systems via switching control [J], Systems and Control Letters,2006,55(11):879-886.
[101]Zhao, J., Hill, D. J., Dissipativity theory for switched systems [J], Automatic Con-trol, IEEE Transactions on,2008,53(4):941-953.
[102]Zhao, J., Hill, D. J., Passivity and stability of switched systems:a multiple storage function method [J], Systems and Control Letters,2008,57(2):158-164.
[103]Zhao, J., Hill, D. J., A notion of passivity for switched systems with state-dependent switching [J], Journal of Control Theory and Applications,2006,4(1): 70-75.
[104]Zhang, L., Gao, H., Asynchronously switched control of switched linear systems with average dwell time [J], Automatica,2010,46(5):953-958.
[105]Zhang, L., Shi, P., Stability, L2-gain and asynchronous control of discrete-time switched systems with average dwell time [J], Automatic Control, IEEE Transac-tions on,2009,54(9):2192-2199.
[106]Wang, Y. E., Sun, X. M., Zhao, J., Asynchronous H∞ control of switched delay sys-tems with average dwell time [J], Journal of the Franklin Institute,2012,349(10): 3159-3169.
[107]Zhao, X., Shi, P., Zhang, L., Asynchronously switched control of a class of slowly switched linear systems [J], Systems and Control Letters,2012,61 (12):1151-1156.
[108]Xie, D., Wang, L., Hao, F., et al., Robust stability analysis and control synthe-sis for discrete-time uncertain switched systems [C], Decision and Control,2003. Proceedings.42nd IEEE Conference on. IEEE,2003,5:4812-4817.
[109]Lin, J., Fei, S., Wu, Q., Reliable H∞ filtering for discrete-time switched singu-lar systems with time-varying delay [J], Circuits, Systems, and Signal Processing, 2012,31(3):1191-1214.
[110]Du, D., Zhou, S., Zhang, B., Generalized H2 output feedback controller design for uncertain discrete-time switched systems via switched Lyapunov functions [J], Nonlinear Analysis:Theory, Methods and Applications,2006,65(11):2135-2146.
[111]Liberzon, D., Switching in systems and control [M], Springer,2003.
[112]Duarte-Mermoud M A, Ordonez-Hurtado R H, Zagalak P. A method for deter-mining the non-existence of a common quadratic Lyapunov function for switched linear systems based on particle swarm optimisation [J], International Journal of Systems Science,2012,43(11):2015-2029.
[113]Sun, X. M., Wang, W, Integral input-to-state stability for hybrid delayed systems with unstable continuous dynamics [J], Automatica,2012,48(9):2359-2364.
[114]Sun, X. M., Liu, G. P., Wang, W., et al., Stability analysis for systems with large delay period:a switching method [J], International Journal of Innovative Comput-ing, Information and Control,2012,8(6):4235-4247.
[115]Niu, B., Zhao, J., Tracking control for output-constrained nonlinear switched sys-tems with a barrier Lyapunov function [J], International Journal of Systems Sci-ence,2013,44(5):978-985.
[116]Wang, Y., Shi, X., Zuo, Z., et al., On finite-time stability for nonlinear impulsive switched systems [J], Nonlinear Analysis:Real World Applications,2013,14(1): 807-814.
[117]Wicks, M., Peleties, P., DeCarlo, R., Switched controller synthesis for the quadratic stabilisation of a pair of unstable linear systems [J], European Journal of Control, 1998,4(2):140-147.
[118]Lien, C. H., Yu, K. W., Chung, Y. J., et al., Switching signal design for global exponential stability of uncertain switched nonlinear systems with time-varying delay [J], Nonlinear Analysis:Hybrid Systems,2011,5(1):10-19.
[119]Phat, V. N., Botmart, T., Niamsup, P., Switching design for exponential stability of a class of nonlinear hybrid time-delay systems [J], Nonlinear Analysis:Hybrid Systems,2009,3(1):1-10.
[120]Sun, X. M., Wang, W., Liu, G. P., et al., Stability analysis for linear switched systems with time-varying delay [J], Systems, Man, and Cybernetics, Part B:Cy-bernetics, IEEE Transactions on,2008,38(2):528-533.
[121]Polderman, J. W., Langerak, R., Stability and robustness of planar switching linear systems [J], Systems and Control Letters,2012,61(9):904-910.
[122]Li, T. F., Dimiro vski, G. M., Liu, Y., et al., Improved stability of a class of switched neutral systems via Lyapunov-Krasovskii functionals and an average dwell-time scheme [J], International Journal of systems science,2013,44(6):1076-1088.
[123]Guckenheimer, J., Holmes, P., Nonlinear oscillations, dynamical systems, and bi-furcations of vector fields [M], Springer Verlag:New York,1983.
[124]Horn, R. A., Johnson, C. R., Matrix analysis [M], Cambridge university press, 2012.
[125]Bhatia, R., Matrix analysis [M], Springer,1997.
[126]Zhao, X., Zhang, L., Shi, P., et al., Stability and stabilization of switched linear systems with mode-dependent average dwell time [J], Automatic Control, IEEE Transactions on,2012,57(7):1809-1815.
[127]Zhang, J., Han, Z., Zhu, F., et al., Stability and stabilization of positive switched systems with mode-dependent average dwell time [J], Nonlinear Analysis:Hybrid Systems,2013,9:42-55.
[128]Yu, Q., Wu, B., Robust stability analysis of uncertain switched linear systems with unstable subsystems [J], International Journal of Systems Science,2013 (ahead-of-print):1-10.
[129]Hernandez-Vargas, E., Colaneri, P., Middleton, R., et al., Discrete□time control for switched positive systems with application to mitigating viral escape [J], Inter-national Journal of Robust and Nonlinear Control,2011,21(10):1093-1111.
[130]Du, D., Jiang, B., Shi, P., et al., Hoo filtering of discrete-time switched systems with state delays via switched Lyapunov function approach [J], Automatic Control, IEEE Transactions on,2007,52(8):1520-1525.
[131]Geromel, J. C., Colaneri, P., Stability and stabilization of discrete time switched systems [J], International Journal of Control,2006,79(7):719-728.
[132]Sun, Y. G., Wang, L., Xie, G., Delay-dependent robust stability and stabilization for discrete-time switched systems with mode-dependent time-varying delays [J], Applied Mathematics and Computation,2006,180(2):428-435.
[133]Lyapunov, A. M., The general problem of the stability of motion [J], International Journal of Control,1992,55(3):531-534.
[134]Passino, K. M., Michel, A. N., Antsaklis, P. J., Lyapunov stability of a class of discrete event systems [J], Automatic Control, IEEE Transactions on,1994,39(2): 269-279.
[135]Upadhyay, R. K., Iyengar, S. R. K., Rai, V., Stability and complexity in ecological systems [J], Chaos, Solitons and Fractals,2000,11(4):533-542.
[136]Wang, Y, Shi, X., Zuo, Z., et al. On finite-time stability for nonlinear impulsive switched systems [J], Nonlinear Analysis:Real World Applications,2013,14(1): 807-814.
[137]Sun, X. M., Wang, W, Integral input-to-state stability for hybrid delayed systems with unstable continuous dynamics [J], Automatica,2012,48(9):2359-2364.
[138]Aleksandrov, A. Y, Kosov, A. A., Platonov, A. V., On the asymptotic stability of switched homogeneous systems [J], Systems and Control Letters,2012,61(1): 127-133.
[139]Clegg, J. C., A nonlinear integrator for servomechanisms [J], American Institute of Electrical Engineers, Part II:Applications and Industry, Transactions of the,1958, 77(1):41-42.
[140]Banos, A., Barreiro, A., Stability of Reset Control Systems [M], Reset Control Systems. Springer London,2012:93-145.
[141]Nesic, D., Zaccarian, L., Teel, A. R., Stability properties of reset systems [J], Au-tomatica,2008,44(8):2019-2026.
[142]Banos, A., Carrasco, J., Barreiro, A., Reset times-dependent stability of reset con-trol with unstable base systems[C], Industrial Electronics,2007. ISIE 2007. IEEE International Symposium on. IEEE,2007:163-168.
[143]Guo, Y, Gui, W., Yang, C., et al., Stability analysis and design of reset control systems with discrete-time triggering conditions [J], Automatica,2012,48(3):528-535.
[144]玉强,吴保卫.一类正线性系统的整体性质[J],云南大学学报：自然科学版,2014,36(1)：6-11.
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