一类改进的离散网络控制系统的稳定性准则
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摘要
在现有研究成果的基础上,针对网络控制系统中存在的网络诱导时滞问题进行了研究。通过引入增广矩阵和三重求和项,构造出一个改进的Lyapunov泛函;并采用离散状态下的Wirtinger不等式对得到的差分项进行处理;最终结果引入凸组合来界定,获得具有更小保守性的稳定性准则。最后,通过数值示例验证了该准则的有效性。
Based on the existing research results,the problem of a class of network-induced delay in networked control systems is studied.An improved Lyapunov functional is constructed by introducing the augmented matrix and three harmonic terms;the differential terms are treated with the Wirtinger inequality under the discrete state;the final result is defined by the convex combination,and the stability criterion with smaller conservatism is obtained.Finally,a numerical example is given to illustrate the effectiveness of the proposed criterion.
Based on the existing research results,the problem of a class of network-induced delay in networked control systems is studied.An improved Lyapunov functional is constructed by introducing the augmented matrix and three harmonic terms;the differential terms are treated with the Wirtinger inequality under the discrete state;the final result is defined by the convex combination,and the stability criterion with smaller conservatism is obtained.Finally,a numerical example is given to illustrate the effectiveness of the proposed criterion.
引文
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[9]SEURET A,GOUAISBAUT F,FRIDMAN E.Stability of discrete-time systems with time-varying delays via a novel summation inequality[J].IEEE Transactions on Automatic Control,2015,60(10):2740-2745.
[10]NAM P T,PATHIRANA P N,TRINH H.Discrete wirtinger-based inequality and its application[J].Journal of the Franklin Institute,2015,352(5):1893-1905.
[11]唐超超,姜偕富,范化续,等.一类线性离散网络控制系统的稳定性准则[J].杭州电子科技大学学报(自然科学版),2017,37(6):41-47.
[2]游科友,谢立华.网络控制系统的最新研究综述[J].自动化学报,2013,39(2):101-118.
[3]LI Y H,JIANG X F.Delay-dependent H∞feedback control for discrete-time networked control systems[C]//Control and Decision Conference(CCDC),2012 24th Chinese.IEEE,2012:1858-1862.
[4]KWON O M,PARK M J,PARK J H,et al.Improved robust stability criteria for uncertain discrete-time systems with interval time-varying delays via new zero equalities[J].IET Control Theory&Applications,2012,6(16):2567-2575.
[5]LIN W J,HE Y,ZHANG C K,et al.Stability analysis of recurrent neural networks with interval time-varying delay via free-matrix-based integral inequality[J].Neurocomputing,2016,205:490-497.
[6]JIANG X F,HAN Q L,YU X H.Stability criteria for linear discrete-time systems with interval-like time-varying delay[C]//American Control Conference,2005.Proceedings of the 2005.IEEE,2005:2817-2822.
[7]KWON O M,PARK M J,PARK J H,et al.Stability and stabilization for discrete-time systems with time-varying delays via augmented Lyapunov-Krasovskii functional[J].Journal of the Franklin Institute,2013,350(3):521-540.
[8]ZHANG B,XU S,ZOU Y.Improved stability criterion and its applications in delayed controller design for discretetime systems[J].Automatica,2008,44(11):2963-2967.
[9]SEURET A,GOUAISBAUT F,FRIDMAN E.Stability of discrete-time systems with time-varying delays via a novel summation inequality[J].IEEE Transactions on Automatic Control,2015,60(10):2740-2745.
[10]NAM P T,PATHIRANA P N,TRINH H.Discrete wirtinger-based inequality and its application[J].Journal of the Franklin Institute,2015,352(5):1893-1905.
[11]唐超超,姜偕富,范化续,等.一类线性离散网络控制系统的稳定性准则[J].杭州电子科技大学学报(自然科学版),2017,37(6):41-47.