Finite-time stability of switched linear systems
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- 英文论文题名：Finite-time stability of switched linear systems
- 论文作者：Linlin Hou ; Chuanguang Sun ; Hangli Ren ; Yunliang Wei
- 英文论文作者：Linlin Hou ; Chuanguang Sun ; Hangli Ren ; Yunliang Wei ; School of Control Science and Engineering ; Dalian University of Technology ; School of Information Science and Engineering ; Qufu Normal University ; Basic Teaching Department ; ShanDong Water Conservancy Vocational College ; School of Engineering ; Qufu Normal University ; School of Mathematical Sciences ; Qufu Normal University
- 年：2017
- 作者机构：School of Control Science and Engineering,Dalian University of Technology;School of Information Science and Engineering,Qufu Normal University;Basic Teaching Department,ShanDong Water Conservancy Vocational College;School of Engineering,Qufu Normal University;School of Mathematical Sciences,Qufu Normal University;
- 英文论文关键词：Switched linear systems ; average dwell time ; finite-time stability
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：O231
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：5
- 文件大小：226k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, the problem of finite-time stability is studied for a class of switched linear systems, where some subsystems are not finite-time stable. A novel average dwell time approach for finite-time stability of switched linear systems in which not all subsystems are finite-time stable is first proposed. Moreover, by constructing a new multiple Lyapunov functional, sufficient condition is provided to cope with the problem of finite-time stability for the given systems. Finally, a numerical example is illustrated to show the effectiveness of the proposed results.
In this paper, the problem of finite-time stability is studied for a class of switched linear systems, where some subsystems are not finite-time stable. A novel average dwell time approach for finite-time stability of switched linear systems in which not all subsystems are finite-time stable is first proposed. Moreover, by constructing a new multiple Lyapunov functional, sufficient condition is provided to cope with the problem of finite-time stability for the given systems. Finally, a numerical example is illustrated to show the effectiveness of the proposed results.
In this paper, the problem of finite-time stability is studied for a class of switched linear systems, where some subsystems are not finite-time stable. A novel average dwell time approach for finite-time stability of switched linear systems in which not all subsystems are finite-time stable is first proposed. Moreover, by constructing a new multiple Lyapunov functional, sufficient condition is provided to cope with the problem of finite-time stability for the given systems. Finally, a numerical example is illustrated to show the effectiveness of the proposed results.
引文
[1]D.Liberzon,A.S.Morse,Basic problems in stability and design of switched systems,IEEE Control Systems Magazine19(5)(1999)59–70.
[2]H.Lin,P.J.Antsaklis,Stability and stabilizability of switched linear systems:a survey of recent results,IEEE Transactions on Automatic Control 54(2)(2009)308–322.
[3]L.Hou,G.Zong,Y.Wu,Y.Cao,Exponential l2-l∞output tracking control for discrete-time switched system with timevarying delay,International Journal of Robust and Nonlinear Control 22(11)(2012)1175–1194.
[4]Y.E.Wang,J.Zhao,B.Jiang,Stabilization of a class of switched linear neutral systems under asynchronous switching,IEEE Transactions on Automatic Control 58(8)(2013)2114–2119.
[5]L.I.Allerhand,U.Shaked,Robust state-dependent switching of linear systems with dwell time,IEEE Transactions on Automatic Control 58(4)(2013)994–1001.
[6]M.Fiacchini,Jungers,Necessary and sufficient condition for stabilizability of discrete-time linear switched systems:a settheory approach,Automatica 50(1)(2014)75–83.
[7]X.Zhao,H.Liu,J.Zhang,H.Li,Multiple-mode observer design for a class of switched linear systms,IEEE Transactions on Automation Science and Engineering 12(1)(2015)272–280.
[8]G.S.Deaecto,M.Souza,J.C.Gernmel,Discrete-time switched linear systems state feedback design with application to network control,IEEE Transactions on Automatic Control 60(3)(2015)877–881.
[9]P.Dorato,Short time stability in linear time-varying systems,Tech.rep.,DTIC Document(1961).
[10]F.Amato,M.Ariola,Finite-time control of discrete-time linear systems,IEEE Transactions on Automatic control 50(5)(2005)724–729.
[11]J.Fu,R.Ma,T.Chai,Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers,Automatica 54(2015)360–373.
[12]H.Du,X.Lin,S.Li,Finite-time boundedness and stabilization of switched linear systems,Kybernetika 46(5)(2010)870–889.
[13]X.Lin,H.Du,S.Li,Finite-time boundedness and l 2-gain analysis for switched delay systems with norm-bounded disturbance,Applied Mathematics and Computation 217(12)(2011)5982–5993.
[14]H.Liu,Y.Shen,X.Zhao,Finite-time stabilization and boundedness of switched linear system under state-dependent switching,Journal of the Franklin Institute 350(3)(2013)541–555.
[15]X.Lin,S.Li,Y.Zou,Finite-time stability of switched linear systems with subsystems which are not finite-time stable,IET Control Theory and Applications 8(12)(2014)1137–1146.
[16]G.Zong,H.Ren,L.Hou,Finite-time stability of interconnected impulsive switched systems,IET Control Theory&Applications 10(6)(2016)648–654.
[17]X.Zhao,Y.Yin,B.Niu,X.Zheng,Stabilization for a class of switched nonlinear systems with novel average dwell time switching by T-S fuzzy modeling,IEEE Transactions on Cybernetics 46(8)(2016)1952–1957.
[18]W.H.Chen,W.X.Zheng,Delay-independent minimum dwell time for exponential stability of uncertain switched delay systems,IEEE Transactions on Automatic Control55(10)(2010)2406–2413.
[2]H.Lin,P.J.Antsaklis,Stability and stabilizability of switched linear systems:a survey of recent results,IEEE Transactions on Automatic Control 54(2)(2009)308–322.
[3]L.Hou,G.Zong,Y.Wu,Y.Cao,Exponential l2-l∞output tracking control for discrete-time switched system with timevarying delay,International Journal of Robust and Nonlinear Control 22(11)(2012)1175–1194.
[4]Y.E.Wang,J.Zhao,B.Jiang,Stabilization of a class of switched linear neutral systems under asynchronous switching,IEEE Transactions on Automatic Control 58(8)(2013)2114–2119.
[5]L.I.Allerhand,U.Shaked,Robust state-dependent switching of linear systems with dwell time,IEEE Transactions on Automatic Control 58(4)(2013)994–1001.
[6]M.Fiacchini,Jungers,Necessary and sufficient condition for stabilizability of discrete-time linear switched systems:a settheory approach,Automatica 50(1)(2014)75–83.
[7]X.Zhao,H.Liu,J.Zhang,H.Li,Multiple-mode observer design for a class of switched linear systms,IEEE Transactions on Automation Science and Engineering 12(1)(2015)272–280.
[8]G.S.Deaecto,M.Souza,J.C.Gernmel,Discrete-time switched linear systems state feedback design with application to network control,IEEE Transactions on Automatic Control 60(3)(2015)877–881.
[9]P.Dorato,Short time stability in linear time-varying systems,Tech.rep.,DTIC Document(1961).
[10]F.Amato,M.Ariola,Finite-time control of discrete-time linear systems,IEEE Transactions on Automatic control 50(5)(2005)724–729.
[11]J.Fu,R.Ma,T.Chai,Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers,Automatica 54(2015)360–373.
[12]H.Du,X.Lin,S.Li,Finite-time boundedness and stabilization of switched linear systems,Kybernetika 46(5)(2010)870–889.
[13]X.Lin,H.Du,S.Li,Finite-time boundedness and l 2-gain analysis for switched delay systems with norm-bounded disturbance,Applied Mathematics and Computation 217(12)(2011)5982–5993.
[14]H.Liu,Y.Shen,X.Zhao,Finite-time stabilization and boundedness of switched linear system under state-dependent switching,Journal of the Franklin Institute 350(3)(2013)541–555.
[15]X.Lin,S.Li,Y.Zou,Finite-time stability of switched linear systems with subsystems which are not finite-time stable,IET Control Theory and Applications 8(12)(2014)1137–1146.
[16]G.Zong,H.Ren,L.Hou,Finite-time stability of interconnected impulsive switched systems,IET Control Theory&Applications 10(6)(2016)648–654.
[17]X.Zhao,Y.Yin,B.Niu,X.Zheng,Stabilization for a class of switched nonlinear systems with novel average dwell time switching by T-S fuzzy modeling,IEEE Transactions on Cybernetics 46(8)(2016)1952–1957.
[18]W.H.Chen,W.X.Zheng,Delay-independent minimum dwell time for exponential stability of uncertain switched delay systems,IEEE Transactions on Automatic Control55(10)(2010)2406–2413.