几类具有时滞的切换系统的稳定性分析与控制
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摘要
切换系统是一类重要的混杂系统,它由多个子系统以及作用在其中的切换规则构成。由于切换系统具有广泛的实际应用背景,所以对它的理论研究具有深远的意义。本文研究了几类时滞切换系统的稳定与控制,主要工作如下:
(1)针对具有时变时滞的线性切换系统,在控制输入和状态都具有时滞的情况下,研究这类系统的鲁棒H∞控制问题。
(2)利用积分不等式和引入自由权矩阵的方法,研究一类不确定变时滞切换系统的鲁棒H∞控制问题。此方法只要求时滞函数上方有界,不需要时滞函数的导数信息。
(3)研究一类具有不确定和多时滞的线性离散切换系统的鲁棒H∞问题。基于多Lyapunov函数法,以线性矩阵不等式形式给出了在任意切换信号作用下离散时滞切换系统具有H∞性能的充分条件,同时给出了切换系统有记忆状态反馈H∞控制设计的一种方案。
(4)研究了一类具有不确定性并带有中立型时滞的线性切换系统的鲁棒H∞控制问题。利用Lyapunov稳定理论和线性矩阵不等式理论,给出了系统满足H∞性能充分条件,并设计线性有记忆反馈控制器以及切换策略。
(5)针对一类由任意有限多个时滞奇异子系统组成的切换系统,研究系统的状态反馈H∞控制问题,利用Lyapunov函数方法和凸组合技术。以LMI的形式给出了在切换状态反馈控制策略下,系统实现状态反馈H∞控制的充分条件。进而给出了切换律和状态反馈H∞切换控制器的设计方案。仿真算例说明控制器设计方案的可行性与有效性。
Switched systems are one kind of the important classes of hybrid systems, which consist of a lot of subsystems and switching sequence. There is great signification in theoretical study because of a lot of application in engineering. Stability and H∞control for classes of switched systems are discussed. The main contributions of this paper are as follows.
(1) The robust H∞control problem for a class of switched linear systems with time delayed states and inputs is discussed.
(2) To uncertain time-varying linear switched systems, the problem of robust H∞controller design is studied by using integral inequality and free-weighting matrix method. It depends on size of delay and requires no information about the derivate of time-delay.
(3) The analysis and synthesis of H∞control via state feedback for discrete switched systems with multiple time delay subsystems are studied. Based on multiple Lyapunov functions theory, a new sufficient condition in form of LMI is derived for the H∞performance analysis under arbitrary switching. the robust state-feedback memory controllers are designed
(4) Robust H∞feedback for a class of switched systems with uncertainties and neutral time-delays is considered . The systems contain uncertainties not only in the state matrices, but also in the time-delay matrices. Based on Lyapunov theory and linear matrix inequalities, the robust state-feedback memory controllers are designed. With the given switching laws, the controllers can guarantee that the states of systems are robust stable.
(5) The state feedback H∞control problem for switched singular systems with delays in both state and control is researched. Based on Lyapunov function approaches and convex combinations techniques, a LMI-based sufficient condition is given for the system implementation of state feedback H∞control .Furthermore, switching law and state feedback H∞controller are designed. A simulation example illustrates the feasibility and effectiveness of the designed controller.
(1)针对具有时变时滞的线性切换系统,在控制输入和状态都具有时滞的情况下,研究这类系统的鲁棒H∞控制问题。
(2)利用积分不等式和引入自由权矩阵的方法,研究一类不确定变时滞切换系统的鲁棒H∞控制问题。此方法只要求时滞函数上方有界,不需要时滞函数的导数信息。
(3)研究一类具有不确定和多时滞的线性离散切换系统的鲁棒H∞问题。基于多Lyapunov函数法,以线性矩阵不等式形式给出了在任意切换信号作用下离散时滞切换系统具有H∞性能的充分条件,同时给出了切换系统有记忆状态反馈H∞控制设计的一种方案。
(4)研究了一类具有不确定性并带有中立型时滞的线性切换系统的鲁棒H∞控制问题。利用Lyapunov稳定理论和线性矩阵不等式理论,给出了系统满足H∞性能充分条件,并设计线性有记忆反馈控制器以及切换策略。
(5)针对一类由任意有限多个时滞奇异子系统组成的切换系统,研究系统的状态反馈H∞控制问题,利用Lyapunov函数方法和凸组合技术。以LMI的形式给出了在切换状态反馈控制策略下,系统实现状态反馈H∞控制的充分条件。进而给出了切换律和状态反馈H∞切换控制器的设计方案。仿真算例说明控制器设计方案的可行性与有效性。
Switched systems are one kind of the important classes of hybrid systems, which consist of a lot of subsystems and switching sequence. There is great signification in theoretical study because of a lot of application in engineering. Stability and H∞control for classes of switched systems are discussed. The main contributions of this paper are as follows.
(1) The robust H∞control problem for a class of switched linear systems with time delayed states and inputs is discussed.
(2) To uncertain time-varying linear switched systems, the problem of robust H∞controller design is studied by using integral inequality and free-weighting matrix method. It depends on size of delay and requires no information about the derivate of time-delay.
(3) The analysis and synthesis of H∞control via state feedback for discrete switched systems with multiple time delay subsystems are studied. Based on multiple Lyapunov functions theory, a new sufficient condition in form of LMI is derived for the H∞performance analysis under arbitrary switching. the robust state-feedback memory controllers are designed
(4) Robust H∞feedback for a class of switched systems with uncertainties and neutral time-delays is considered . The systems contain uncertainties not only in the state matrices, but also in the time-delay matrices. Based on Lyapunov theory and linear matrix inequalities, the robust state-feedback memory controllers are designed. With the given switching laws, the controllers can guarantee that the states of systems are robust stable.
(5) The state feedback H∞control problem for switched singular systems with delays in both state and control is researched. Based on Lyapunov function approaches and convex combinations techniques, a LMI-based sufficient condition is given for the system implementation of state feedback H∞control .Furthermore, switching law and state feedback H∞controller are designed. A simulation example illustrates the feasibility and effectiveness of the designed controller.
引文
[1]周均鸿.切换系统的稳定性分析与设计[D].台湾:国立中央大学,2006:
[2] Witsenhausen H S.A class of hybrid-state continuous-time dynamic systems[J].IEEE Trans onAutomatic Control,1966,11(6):665-683.
[3] Cellier F E.Combined continuous\discrete system simulation by use of digital computer: Technique and tools[D].Zurich,Switzerland:Swiss Federal Institute of Technology,1979:
[4] Golli A,Varaiya P.Hybrid dynamical systems[A].In Proc of the 28th IEEE Conference onDecision and Control[C],Tampa,Florida,USA,1989:2708-2712.
[5]李浚圣.线性切换系统的最优切换律[D].沈阳:东北大学,2005:
[6] Liberzon D, Morse A S.Basic problems in stability and design of switched systems[J].ControlSystem Magazine,1999,19(5):58-70.
[7] Liberzon D.Switchingin systems and Control [M]. Birkhauser, Boston, 2003.
[8]孙希明.切换时滞系统的稳定性分析[D].沈阳:东北大学,2006:
[9] Branicky M S, Multiple Lyapunov Functions and Other Analysis Tool for Switched and Hybrid Systems [J]. IEEE Trans on Automatic Control ,1998,43(4):475-482.
[10] Liberzon D. Switching in Systems and Control [M]. Boston: Birkhauser, 2003.
[11] Sun Z D, Ge S S. Switched Linear Systems Control and Design [M], New York: Springer-verlag, 2004.
[12] Zhao J, Spong M W. Hybrid Control for Global Stabilization of the cart-pendulum System [J]. Automatica, 2001, 37(12):1941-1951.
[13] Zhao J, Dimirovski G M. Quadratic Stability of a class of Switched Nonlinear Systems [J]. IEEE Trans on Automatic Control, 2004, 49(4):574-578.
[14]刘洪刚,付主木,高爱云.不确定切换时滞线性系统的状态反馈鲁棒H∞控制[J].河南科技大学学报:自然科学版,2008,29(4):69-72.
[15]孙文安,赵植武,董世山,张强.一类不确定离散时滞切换系统H∞的二次稳定性[J].工程数学学报,2007,24(5):825-832.
[16]罗跃生,董晓璋,孙明丽.不确定变时滞系统的鲁棒非脆弱H∞控制[J].控制工程,2008,15(3):265-268.
[17]聂宏,赵军,王明顺。线性不确定时滞系统混杂反馈H∞鲁棒镇定[J].控制与决策,2004.19(6):642-646.
[18] Nie H, Zhao J. Hybrid state feedback H∞robust control for a class of linear systems with norm-bound uncertainty[C]. Rro. Of the A. C. C. Denver, Colorado, 2003.
[19] Kim J K, Park H B. H∞state feedback control for generalized continuous/discrete time-delay system [J]. Automatica, 1999, 35(8):1443-1451.
[20] Hui G D.Simple criteria for stability of neutral systems with multiple delays [J].Int.J. Sys.Sci. 1997, 28 (12):1325一1328.
[21] Mahmoud M S.Robust H∞control of linear neutral systems[J].Automatica ,2000,36(5):757一764.
[22] Guckenheimer J.. A robust hybrid stabilization strategy for equilibria[J].IEEE Transactions on Automatic Control,1995,40(2):321-326.
[23] Phat Vu N..Robust Stability and Stabilizability of Uncertain Linear Hybrid Systems With State Delays [J].IEEE Transactions on Circuits and Systems一Ⅱ:ExPress Briefs,2005,52(2):94一98.
[24] Horn C,Ramadge P.J..Robustness issues for hybrid systems[A].In Proceedings of the 34th CDC[C], New Orleans,USA,1995:1467-1472.
[25] Lemmon M.D,Bett C..Hybrid control system design using robust linear control agents[A].In Proceedings of the 34th CDC[C],New Orleans,USA,1995:2688-2693.
[26] E. K. Boukas, H.Yang. Exponential stabilizability of stochastic systems with Markovian jumping parameters[J]. Automatica, 1999,35: 1437-1441.
[27] Lall S.G., Dullerud G.E., H∞synthesis for multi-rate hybrid systems[A].Proceedings of the 36th CDC[C],San Diego,USA,1997:2035-2040.
[28] Dullerud G.E.,Lall S.G.. H∞synthesis for hybrid systems with jumps[A].Proceedings of American Control conference[C],Albuquerque,New Mexico,1997:1672-1676.
[29]张霄力,赵军.任意切换下不确定线性切换系统的鲁棒镇定[J].自动化学报, 2002, 28(5): 859-861.
[30]董学平,王执铨.一类不确定非线性切换系统的鲁棒容错控制[J].控制与决策,2009,24(6):916-920.
[31]张霓,吴铁军.参数摄动混杂离散系统的鲁棒稳定性[J].控制理论与应用.2002,19(5):731-736.
[32]连捷,赵军.一类不确定线性切换系统的鲁棒H∞滑模控制[J].控制理论与应用,2008:25(3):492-496.
[33]谢广明,郑大钟.切换规则不确定线性切换系统的鲁棒稳定性[J].清华大学学报(自然科学版),2002,42(3):396-402.
[34]付主木,费树岷,龙飞,丛屾.不确定切换系统的动态输出反馈鲁棒H_∞控制[J].东南大学学报(自然科学版), 2007,37(1):153-158.
[35]赵胜芝,赵军,张庆灵,付俊.不确定非线性切换系统的鲁棒H_∞控制[J].控制理论与应用, 2006,23(4):606-610.
[36]李莉莉,冯佳昕,赵军。一类非线性切换系统的非脆弱鲁棒H_∞控制[J].东北大学学报(自然科学版),2009,30(4):471-474
[37]宋政一,赵军.不确定时滞线性离散切换系统鲁棒H_∞控制[J].自动化学报,2006,32(5):760-766.
[38] Sun Xi-Ming, Zhao Jun, Hill David J..Stability and L 2-gain analysis for switched delay systems: a delay-dependent method [J].Automatica, 2006, 42: 1769-1774 .
[39] Sun Yuan Gong, Wang Long, Xie Guangming. Delay-dependent robust stability and stabilization for discrete-time switched systems with mode-dependent time-varying delays [J]. Applied Mathematics and computation 2006, 180: 428-435.
[40] Kim S, Campbell S A, Liu X Z, Stability of a class of linear Switching Systems with Time Delay[J]. IEEE Trans on Circuits and Systems-I:Regular Papers,2006,53(2):384-393.
[41] Wang Y J, Xie G M,Wang L,Controllabiliity of Switched Time-delay Systems Under Constrained Switching[J].Journal of Math Analysis Application,2003,286(2):397-421.
[42] Xie G,Wang L.Controllability of Switched Linear Discrete-time Systems With Time Delay[J]//proc of the American Control conference,Denver,USA,2003,4:2797-2802.
[43] Sun Y G, Wang L, Xie G M. Stability of Switched Systems with Time-Varying Delays: Delay-dependent Common Luapunov Function-of Apporpach[c]//proc of the American Control Conference, Minneapolis,Minnesota,USA,2006,1544-1549.
[44]刘洪刚,付主木,高爱云.不确定切换时滞线性系统的状态反馈鲁棒H∞控制[J].河南科技大学学报:自然科学版,2008,29(4):69-72.
[45]孙文安,赵植武,董世山,张强.一类不确定离散时滞切换系统H∞的二次稳定性[J].工程数学学报,2007,24(5):825-832.
[46] S.H.Lee, T.H.Kim &J.T.Lim. A new stability of switched systems[J]. Automatica,2000,36,917-922.
[47]王仁明,关治洪,刘新芝.具有输入时滞的切换系统的稳定性分析与控制[J].三峡大学学报(自然科学版)2004,26(2):170-172.
[48] J.L.Aguilar & R.A.Garcia. An extension of LaSalle’s invariance principle for switched systems[J] Systems & Control Letters,2006,55:376-384.
[49] J.P, Hespanha, D.Liberzon, D.Angeli & E.D.Songtag.Nonlinear norm-observability notions and stability of switched systems[J],IEEE Transactions on Automatic Control 2005,50(7),154-168.
[50]罗跃生,董晓璋,孙明丽.不确定变时滞系统的鲁棒非脆弱H∞控制[J].控制工程,2008,15(3):265-268.
[51] xie L. Output feedback H∞control of systems with parameter uncertainty[J].In J Control,1996,63(4):741-750.
[52] Kwon O M, Park J H.Guaranteed cost control of time-delay chaotic systems [J].Chaos,Solitions and Fractals,2006,27(4):1108-1118.
[53] Daafouz J, Riedinger P,Iung C, Stability analysis and control synthesis for switched Lyapunov function approach [J].IEEE Transactions on Automatic Control,2002,47(11):1883-1887.
[54]孙文安,沈连山,邹开其,李不贤.一类不确定离散时滞切换系统的二次保成本控制[J] .应用科学学报,2006,24(2):1 81-1 86.
[55]张颖,段广仁,贺亮.一类含有时滞的离散切换系统鲁棒稳定性分析[J] .吉林大学学报(工学版) ,2006,36(5):740一744.
[56] D Xie,L Wang,F Hao,et al .An LMI approach to L2 gain analysis and control synthesis of uncertain switched systems [J].IEEE Proceedings on Control Theory and Applications,2004.151(1):21-28.
[57] D Xie,L Wang,G Xie,et al.An LMI approach to L2 gain analysis and control synthesis of switched systems [A].2004 IEEE International Symposium on Conmputer Aided Control Systems Design [C].Taipei ,Taiwan:IEEE,2004,350-355.
[58] D Xie,L Wang.An LMI approach to L2 gain analysis of uncertain switched systems [A].IEEE International Conference on Systems.Man and Cybernetics [C].Washingtion.DC,USA:IEEE,2003,2278-2283.
[59] ZHAI G S,SUN Y,CHEN X K,et al.Stability and L2 gain analysis for switchedsymmetric systems with time delay [A].Proceedings of the 2003 American Control Conference [C].Denver, Colorado:IEEE,2003,2682-2687.
[60]卢建宁,张彦虎,赵光宙。离散时滞切换系统的无记忆状态反馈镇定[J].控制与决策,2006,21(8):941-944.
[61]石胜利,杨军,华长春,王利魁.时滞依赖型中立系统的鲁棒稳定性分析[J].纯粹数学与应用数学,2007,23(2):243-248.
[62]李宏飞,周军.时变线性中立型系统的鲁棒H∞性能[J]应用数学,2007,20(3):621-626.
[63]孙希明,付俊,孙洪飞,赵军。一类切换线性中立时滞系统稳定性的分析[J]中国电机工程学报,2005:25(23)42-46.
[64]张榆平,切换中立型系统稳定性分析与设计的若干问题研究[D].电子科技大学。
[65]林安辉,张霄力。一类带有中立型时滞的线性切换系统的鲁棒镇定[J],2008,36卷增刊157-160.
[66]孟斌,张继峰.切换线性奇异系统能达的必要条件[J].航空学报,2005,26(2):224-228.
[67] Meng B, Zhang J F. Admissible switched control of singular systems[A]. Proc of the 23rd Chinese Control Conference[C].Wuxi Shanghai,China:East China University of Science and Technology Press,2004:1615-1619.
[68]付主木,费树岷,薄煜明,李涛。一类不确定切换奇异系统的鲁棒H∞控制[J]。南京理工大学学报(自然科学版),2008,32(3):269-273.
[69]付主木,吴庆涛,费树岷。一类切换时滞奇异系统的状态反馈H∞控制[J]。计算机应用研究,2008,25(7):2013-2015.
[70]韩丽丽。切换时滞系统的鲁棒H∞控制[D].内蒙古:内蒙古师范大学,2007:
[2] Witsenhausen H S.A class of hybrid-state continuous-time dynamic systems[J].IEEE Trans onAutomatic Control,1966,11(6):665-683.
[3] Cellier F E.Combined continuous\discrete system simulation by use of digital computer: Technique and tools[D].Zurich,Switzerland:Swiss Federal Institute of Technology,1979:
[4] Golli A,Varaiya P.Hybrid dynamical systems[A].In Proc of the 28th IEEE Conference onDecision and Control[C],Tampa,Florida,USA,1989:2708-2712.
[5]李浚圣.线性切换系统的最优切换律[D].沈阳:东北大学,2005:
[6] Liberzon D, Morse A S.Basic problems in stability and design of switched systems[J].ControlSystem Magazine,1999,19(5):58-70.
[7] Liberzon D.Switchingin systems and Control [M]. Birkhauser, Boston, 2003.
[8]孙希明.切换时滞系统的稳定性分析[D].沈阳:东北大学,2006:
[9] Branicky M S, Multiple Lyapunov Functions and Other Analysis Tool for Switched and Hybrid Systems [J]. IEEE Trans on Automatic Control ,1998,43(4):475-482.
[10] Liberzon D. Switching in Systems and Control [M]. Boston: Birkhauser, 2003.
[11] Sun Z D, Ge S S. Switched Linear Systems Control and Design [M], New York: Springer-verlag, 2004.
[12] Zhao J, Spong M W. Hybrid Control for Global Stabilization of the cart-pendulum System [J]. Automatica, 2001, 37(12):1941-1951.
[13] Zhao J, Dimirovski G M. Quadratic Stability of a class of Switched Nonlinear Systems [J]. IEEE Trans on Automatic Control, 2004, 49(4):574-578.
[14]刘洪刚,付主木,高爱云.不确定切换时滞线性系统的状态反馈鲁棒H∞控制[J].河南科技大学学报:自然科学版,2008,29(4):69-72.
[15]孙文安,赵植武,董世山,张强.一类不确定离散时滞切换系统H∞的二次稳定性[J].工程数学学报,2007,24(5):825-832.
[16]罗跃生,董晓璋,孙明丽.不确定变时滞系统的鲁棒非脆弱H∞控制[J].控制工程,2008,15(3):265-268.
[17]聂宏,赵军,王明顺。线性不确定时滞系统混杂反馈H∞鲁棒镇定[J].控制与决策,2004.19(6):642-646.
[18] Nie H, Zhao J. Hybrid state feedback H∞robust control for a class of linear systems with norm-bound uncertainty[C]. Rro. Of the A. C. C. Denver, Colorado, 2003.
[19] Kim J K, Park H B. H∞state feedback control for generalized continuous/discrete time-delay system [J]. Automatica, 1999, 35(8):1443-1451.
[20] Hui G D.Simple criteria for stability of neutral systems with multiple delays [J].Int.J. Sys.Sci. 1997, 28 (12):1325一1328.
[21] Mahmoud M S.Robust H∞control of linear neutral systems[J].Automatica ,2000,36(5):757一764.
[22] Guckenheimer J.. A robust hybrid stabilization strategy for equilibria[J].IEEE Transactions on Automatic Control,1995,40(2):321-326.
[23] Phat Vu N..Robust Stability and Stabilizability of Uncertain Linear Hybrid Systems With State Delays [J].IEEE Transactions on Circuits and Systems一Ⅱ:ExPress Briefs,2005,52(2):94一98.
[24] Horn C,Ramadge P.J..Robustness issues for hybrid systems[A].In Proceedings of the 34th CDC[C], New Orleans,USA,1995:1467-1472.
[25] Lemmon M.D,Bett C..Hybrid control system design using robust linear control agents[A].In Proceedings of the 34th CDC[C],New Orleans,USA,1995:2688-2693.
[26] E. K. Boukas, H.Yang. Exponential stabilizability of stochastic systems with Markovian jumping parameters[J]. Automatica, 1999,35: 1437-1441.
[27] Lall S.G., Dullerud G.E., H∞synthesis for multi-rate hybrid systems[A].Proceedings of the 36th CDC[C],San Diego,USA,1997:2035-2040.
[28] Dullerud G.E.,Lall S.G.. H∞synthesis for hybrid systems with jumps[A].Proceedings of American Control conference[C],Albuquerque,New Mexico,1997:1672-1676.
[29]张霄力,赵军.任意切换下不确定线性切换系统的鲁棒镇定[J].自动化学报, 2002, 28(5): 859-861.
[30]董学平,王执铨.一类不确定非线性切换系统的鲁棒容错控制[J].控制与决策,2009,24(6):916-920.
[31]张霓,吴铁军.参数摄动混杂离散系统的鲁棒稳定性[J].控制理论与应用.2002,19(5):731-736.
[32]连捷,赵军.一类不确定线性切换系统的鲁棒H∞滑模控制[J].控制理论与应用,2008:25(3):492-496.
[33]谢广明,郑大钟.切换规则不确定线性切换系统的鲁棒稳定性[J].清华大学学报(自然科学版),2002,42(3):396-402.
[34]付主木,费树岷,龙飞,丛屾.不确定切换系统的动态输出反馈鲁棒H_∞控制[J].东南大学学报(自然科学版), 2007,37(1):153-158.
[35]赵胜芝,赵军,张庆灵,付俊.不确定非线性切换系统的鲁棒H_∞控制[J].控制理论与应用, 2006,23(4):606-610.
[36]李莉莉,冯佳昕,赵军。一类非线性切换系统的非脆弱鲁棒H_∞控制[J].东北大学学报(自然科学版),2009,30(4):471-474
[37]宋政一,赵军.不确定时滞线性离散切换系统鲁棒H_∞控制[J].自动化学报,2006,32(5):760-766.
[38] Sun Xi-Ming, Zhao Jun, Hill David J..Stability and L 2-gain analysis for switched delay systems: a delay-dependent method [J].Automatica, 2006, 42: 1769-1774 .
[39] Sun Yuan Gong, Wang Long, Xie Guangming. Delay-dependent robust stability and stabilization for discrete-time switched systems with mode-dependent time-varying delays [J]. Applied Mathematics and computation 2006, 180: 428-435.
[40] Kim S, Campbell S A, Liu X Z, Stability of a class of linear Switching Systems with Time Delay[J]. IEEE Trans on Circuits and Systems-I:Regular Papers,2006,53(2):384-393.
[41] Wang Y J, Xie G M,Wang L,Controllabiliity of Switched Time-delay Systems Under Constrained Switching[J].Journal of Math Analysis Application,2003,286(2):397-421.
[42] Xie G,Wang L.Controllability of Switched Linear Discrete-time Systems With Time Delay[J]//proc of the American Control conference,Denver,USA,2003,4:2797-2802.
[43] Sun Y G, Wang L, Xie G M. Stability of Switched Systems with Time-Varying Delays: Delay-dependent Common Luapunov Function-of Apporpach[c]//proc of the American Control Conference, Minneapolis,Minnesota,USA,2006,1544-1549.
[44]刘洪刚,付主木,高爱云.不确定切换时滞线性系统的状态反馈鲁棒H∞控制[J].河南科技大学学报:自然科学版,2008,29(4):69-72.
[45]孙文安,赵植武,董世山,张强.一类不确定离散时滞切换系统H∞的二次稳定性[J].工程数学学报,2007,24(5):825-832.
[46] S.H.Lee, T.H.Kim &J.T.Lim. A new stability of switched systems[J]. Automatica,2000,36,917-922.
[47]王仁明,关治洪,刘新芝.具有输入时滞的切换系统的稳定性分析与控制[J].三峡大学学报(自然科学版)2004,26(2):170-172.
[48] J.L.Aguilar & R.A.Garcia. An extension of LaSalle’s invariance principle for switched systems[J] Systems & Control Letters,2006,55:376-384.
[49] J.P, Hespanha, D.Liberzon, D.Angeli & E.D.Songtag.Nonlinear norm-observability notions and stability of switched systems[J],IEEE Transactions on Automatic Control 2005,50(7),154-168.
[50]罗跃生,董晓璋,孙明丽.不确定变时滞系统的鲁棒非脆弱H∞控制[J].控制工程,2008,15(3):265-268.
[51] xie L. Output feedback H∞control of systems with parameter uncertainty[J].In J Control,1996,63(4):741-750.
[52] Kwon O M, Park J H.Guaranteed cost control of time-delay chaotic systems [J].Chaos,Solitions and Fractals,2006,27(4):1108-1118.
[53] Daafouz J, Riedinger P,Iung C, Stability analysis and control synthesis for switched Lyapunov function approach [J].IEEE Transactions on Automatic Control,2002,47(11):1883-1887.
[54]孙文安,沈连山,邹开其,李不贤.一类不确定离散时滞切换系统的二次保成本控制[J] .应用科学学报,2006,24(2):1 81-1 86.
[55]张颖,段广仁,贺亮.一类含有时滞的离散切换系统鲁棒稳定性分析[J] .吉林大学学报(工学版) ,2006,36(5):740一744.
[56] D Xie,L Wang,F Hao,et al .An LMI approach to L2 gain analysis and control synthesis of uncertain switched systems [J].IEEE Proceedings on Control Theory and Applications,2004.151(1):21-28.
[57] D Xie,L Wang,G Xie,et al.An LMI approach to L2 gain analysis and control synthesis of switched systems [A].2004 IEEE International Symposium on Conmputer Aided Control Systems Design [C].Taipei ,Taiwan:IEEE,2004,350-355.
[58] D Xie,L Wang.An LMI approach to L2 gain analysis of uncertain switched systems [A].IEEE International Conference on Systems.Man and Cybernetics [C].Washingtion.DC,USA:IEEE,2003,2278-2283.
[59] ZHAI G S,SUN Y,CHEN X K,et al.Stability and L2 gain analysis for switchedsymmetric systems with time delay [A].Proceedings of the 2003 American Control Conference [C].Denver, Colorado:IEEE,2003,2682-2687.
[60]卢建宁,张彦虎,赵光宙。离散时滞切换系统的无记忆状态反馈镇定[J].控制与决策,2006,21(8):941-944.
[61]石胜利,杨军,华长春,王利魁.时滞依赖型中立系统的鲁棒稳定性分析[J].纯粹数学与应用数学,2007,23(2):243-248.
[62]李宏飞,周军.时变线性中立型系统的鲁棒H∞性能[J]应用数学,2007,20(3):621-626.
[63]孙希明,付俊,孙洪飞,赵军。一类切换线性中立时滞系统稳定性的分析[J]中国电机工程学报,2005:25(23)42-46.
[64]张榆平,切换中立型系统稳定性分析与设计的若干问题研究[D].电子科技大学。
[65]林安辉,张霄力。一类带有中立型时滞的线性切换系统的鲁棒镇定[J],2008,36卷增刊157-160.
[66]孟斌,张继峰.切换线性奇异系统能达的必要条件[J].航空学报,2005,26(2):224-228.
[67] Meng B, Zhang J F. Admissible switched control of singular systems[A]. Proc of the 23rd Chinese Control Conference[C].Wuxi Shanghai,China:East China University of Science and Technology Press,2004:1615-1619.
[68]付主木,费树岷,薄煜明,李涛。一类不确定切换奇异系统的鲁棒H∞控制[J]。南京理工大学学报(自然科学版),2008,32(3):269-273.
[69]付主木,吴庆涛,费树岷。一类切换时滞奇异系统的状态反馈H∞控制[J]。计算机应用研究,2008,25(7):2013-2015.
[70]韩丽丽。切换时滞系统的鲁棒H∞控制[D].内蒙古:内蒙古师范大学,2007: