New Results on Reachable Set Estimation for Singular Systems with Time-Varying Delays
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- 英文论文题名：New Results on Reachable Set Estimation for Singular Systems with Time-Varying Delays
- 论文作者：LIU Guobao ; ZHANG Baoyong ; MA Qian
- 英文论文作者：LIU Guobao ; ZHANG Baoyong ; MA Qian ; School of Automation ; Nanjing University of Science and Technology
- 年：2017
- 作者机构：School of Automation, Nanjing University of Science and Technology;
- 英文论文关键词：Singular systems ; Time-varying delays ; Reachable set estimation ; LMIs
- 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（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 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：6
- 文件大小：1335k
- 原文格式：D
- 会议级别：全国
摘要
This paper deals with the problem of reachable set estimation for singular systems with time-varying delays. Based on the Lyapunov-Krasovskii functional approach and the reciprocally convex inequality, sufficient delay-dependent conditions are obtained in terms of linear matrix inequalities(LMIs) for the existence of an intersection of ellipsoids, which contains the considered system states under zero initial conditions. Furthermore, a new bounding technique is utilized for the fast subsystem without any assumptions on system matrices. The effectiveness of the method is demonstrated by two numerical examples.
This paper deals with the problem of reachable set estimation for singular systems with time-varying delays. Based on the Lyapunov-Krasovskii functional approach and the reciprocally convex inequality, sufficient delay-dependent conditions are obtained in terms of linear matrix inequalities(LMIs) for the existence of an intersection of ellipsoids, which contains the considered system states under zero initial conditions. Furthermore, a new bounding technique is utilized for the fast subsystem without any assumptions on system matrices. The effectiveness of the method is demonstrated by two numerical examples.
This paper deals with the problem of reachable set estimation for singular systems with time-varying delays. Based on the Lyapunov-Krasovskii functional approach and the reciprocally convex inequality, sufficient delay-dependent conditions are obtained in terms of linear matrix inequalities(LMIs) for the existence of an intersection of ellipsoids, which contains the considered system states under zero initial conditions. Furthermore, a new bounding technique is utilized for the fast subsystem without any assumptions on system matrices. The effectiveness of the method is demonstrated by two numerical examples.
引文
[1]S.Boyd,L.El Ghaoui,E.Feron,V.Balakrishnam,Linear Matrix Inequalities In Systems and Control Theory,SIAM:Philadelphia,PA,1994.
[2]E.Fridman,U.Shaked,On reachable sets for linear systems with delay and bounded peak inputs,Automatica,39:2005–2010,2003.
[3]K.Gu,V.L.Kharitonov,J.Chen,Stability of Time-Delay Systems,Birkh aüser,Boston,2003.
[4]J.H.Kim,Improved ellipsoidal bound of reachable sets for time-delayed linear systems with disturbances,Automatica,44:2940–2943,2008.
[5]Z.Zuo,D.W.C.Ho,Y.Wang,Reachable set bounding for delayed systems with polytopic uncertainties:the maximal Lyapunov-Krasovskii functional approach,Automatica,46:949–952,2010.
[6]Z.Zuo,D.W.C.Ho,Y.Wang,Reachable set estimation for linear systems in the presence of both discrete and distributed delays,IET Control Theory and Applications,5:1808–1812,2011.
[7]Z.Feng,Lam.J,An improved result on reachable set estimation and synthesis of time-delay systems,Applied Mathematics and Computation,249:89–97,2014.
[8]L.V.Hien,N.T.An,H.Trinh,New results on state bounding for discrete-time systems with interval time-varying delay and bounded disturbance inputs,IET Control Theory and Applications,8:1405–1414,2014.
[9]B.Zhang,J.Lam,S.Xu,Reachable set estimation and controller design for distributed delay systems with bounded disturbances,Journal of the Franklin Institute,351:3068–3088,2014.
[10]B.Zhang,J.Lam,S.Xu,Relaxed results on reachable set estimation of time-delay systems with bounded peak inputs,International Journal of Robust and Nonlinear Control,26:1994–2007,2016.
[11]J.Lam,B.Zhang,Y.Chen,S.Xu,Reachable set estimation for discrete-time linear systems with time delays,International Journal of Robust and Nonlinear Control,25:269–281,2015.
[12]Z.Feng,J.Lam,On reachable set estimation of singular systems,Automatica,52:146–153,2015.
[13]L.Dai,Singular Control Systems,Springer-Verlag,New York,1989.
[14]S.Xu,J.Lam,Robust Control and Filtering of Singular Systems,Springer-Verlag,Berlin,2006.
[15]P.Park,J.W.Ko,C.Jeong,Reciprocally convex approach to stability of systems with time-varying delays,Automatica,47:235–238,2011.
[16]F.Li,X.Zhang,A delay-dependent bounded real lemma for singular LPV systems with time-variant delay,International Journal of Robust and Nonlinear Control,22:559–574,2012.
[2]E.Fridman,U.Shaked,On reachable sets for linear systems with delay and bounded peak inputs,Automatica,39:2005–2010,2003.
[3]K.Gu,V.L.Kharitonov,J.Chen,Stability of Time-Delay Systems,Birkh aüser,Boston,2003.
[4]J.H.Kim,Improved ellipsoidal bound of reachable sets for time-delayed linear systems with disturbances,Automatica,44:2940–2943,2008.
[5]Z.Zuo,D.W.C.Ho,Y.Wang,Reachable set bounding for delayed systems with polytopic uncertainties:the maximal Lyapunov-Krasovskii functional approach,Automatica,46:949–952,2010.
[6]Z.Zuo,D.W.C.Ho,Y.Wang,Reachable set estimation for linear systems in the presence of both discrete and distributed delays,IET Control Theory and Applications,5:1808–1812,2011.
[7]Z.Feng,Lam.J,An improved result on reachable set estimation and synthesis of time-delay systems,Applied Mathematics and Computation,249:89–97,2014.
[8]L.V.Hien,N.T.An,H.Trinh,New results on state bounding for discrete-time systems with interval time-varying delay and bounded disturbance inputs,IET Control Theory and Applications,8:1405–1414,2014.
[9]B.Zhang,J.Lam,S.Xu,Reachable set estimation and controller design for distributed delay systems with bounded disturbances,Journal of the Franklin Institute,351:3068–3088,2014.
[10]B.Zhang,J.Lam,S.Xu,Relaxed results on reachable set estimation of time-delay systems with bounded peak inputs,International Journal of Robust and Nonlinear Control,26:1994–2007,2016.
[11]J.Lam,B.Zhang,Y.Chen,S.Xu,Reachable set estimation for discrete-time linear systems with time delays,International Journal of Robust and Nonlinear Control,25:269–281,2015.
[12]Z.Feng,J.Lam,On reachable set estimation of singular systems,Automatica,52:146–153,2015.
[13]L.Dai,Singular Control Systems,Springer-Verlag,New York,1989.
[14]S.Xu,J.Lam,Robust Control and Filtering of Singular Systems,Springer-Verlag,Berlin,2006.
[15]P.Park,J.W.Ko,C.Jeong,Reciprocally convex approach to stability of systems with time-varying delays,Automatica,47:235–238,2011.
[16]F.Li,X.Zhang,A delay-dependent bounded real lemma for singular LPV systems with time-variant delay,International Journal of Robust and Nonlinear Control,22:559–574,2012.