An improved stability criterion for singular systems with time-varying delay via a relaxed integral inequality
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- 英文论文题名：An improved stability criterion for singular systems with time-varying delay via a relaxed integral inequality
- 论文作者：ZHI Ya-Li ; HE Yong ; WU Min
- 英文论文作者：ZHI Ya-Li ; HE Yong ; WU Min ; School of Automation ; China University of Geosciences ; Hubei key Laboratory of Advanced Control and Intelligent Automation for Complex Systems
- 年：2017
- 作者机构：School of Automation,China University of Geosciences;Hubei key Laboratory of Advanced Control and Intelligent Automation for Complex Systems;
- 英文论文关键词：Stability ; Singular systems with time-varying delay ; Lyapunov-Krasovskii functional ; Relaxed integral inequality
- 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：O175
- 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：4
- 文件大小：195k
- 原文格式：D
- 会议级别：全国
摘要
This paper concerns the stability problem of singular systems with time-varying delay. According to different delaypartition intervals, an augmented Lyapunov-Krasovskii functional with delay cross terms is constructed. Based on it, using the relaxed integral inequality technique is to obtain a less conservative stability criterion. As a result, two numerical examples are provided to demonstrate the effectiveness of the proposed method.
This paper concerns the stability problem of singular systems with time-varying delay. According to different delaypartition intervals, an augmented Lyapunov-Krasovskii functional with delay cross terms is constructed. Based on it, using the relaxed integral inequality technique is to obtain a less conservative stability criterion. As a result, two numerical examples are provided to demonstrate the effectiveness of the proposed method.
This paper concerns the stability problem of singular systems with time-varying delay. According to different delaypartition intervals, an augmented Lyapunov-Krasovskii functional with delay cross terms is constructed. Based on it, using the relaxed integral inequality technique is to obtain a less conservative stability criterion. As a result, two numerical examples are provided to demonstrate the effectiveness of the proposed method.
引文
[1]L.Dai,Singular control systems,Springer,1989.
[2]S.Y.Xu,P.V.Dooren,R.Stefan,J.Lam,Robust stability and stabilization for singular delay systems with state delay and parameter uncertainty,IEEE Transactions on Automatic Control,47(2002)1122-1128.
[3]J.Chen,C.Lin,B.Chen,Q.G.Wang,Output feedback control for singular Markovian jump systems with uncertain transition rates,IET Control Theory and Applications,18(2016)2142-2147.
[4]C.Lin,J.Chen,B.Chen,L.Guo,Z.Zhang,Fuzzy nomalization and stabilization for a class of nonlinear rectangular descriptor systems,Neurocomputing,219(2017)263-268.
[5]L.V.Hien,L.H.Vu,V.N.Phat,Improved delay-dependent exponential stability of singular systems with mixed interval time-varying delays,IET Control Theory and Applications,9(2015)1364-1372.
[6]E.Fridman,Stability of linear descriptor systems with delay:a Lyapunov-based approach,Journal of Mathematical Analysis and Applications,273(2002)24-44.
[7]J.Chen,C.Lin,B.Chen,Q.G.Wang,Mixed H∞and passive control for singular systems with time delay via static output feedback,Applied Mathematics and Computation,293(2017)244-253.
[8]Z.G.Wu,J.H.Park,H.Su,J.Chu,Dissipativity analysis for singular systems with time-varying delays,Applied Mathematics and Computation,218(2011)4605-4613.
[9]H.Chen,P.Hu,New results on exponential stability for singular systems with two interval time-varying delays,IET Control Theory and Applications,15(2013)1941-1949.
[10]Z.Feng,W.Li,J.Lam,New admissibility analysis for discrete singular systems with time-varying delay,Applied Mathematics and Computation,265(2015)1058-1066.
[11]Z.G.Wu,J.H.Park,H.Su,J.Chu,Reliable passive control for singular systems with time-varying delays,Journal of Process Control,23(2013)1217-1228.
[12]X.L.Zhu,Y.Y.Wang,Y.Gan,H∞filtering for continuoustime singular systems with time-varying delay,International Journal of Adaptive Control and Signal Processing,25(2011)137-154.
[13]Y.Ariba,F.Gouaisbaut,An augmented model for robust stability analysis of time-varying delay systems,Internatinal Journal of Control,82(2009)1616-1626.
[14]M.J.Park,O.M.Kwon,J.H.Park,S.M.Lee,A new augmented Lyapunov-Krasovskii functional approach for stability of linear systems with time-varying delays,Applied Mathematics and Computation,217(2011)7197-7209.
[15]Y.He,Q.G.Wang,C.Lin,M.Wu,Augmented Lyapunov functional and delay-dependent stability criteria for neutral systems,International Journal of Robust and Nonlinear Control,15(2005)923-933.
[16]L.L.Liu,J.G.Peng,B.W.Wu,On parameterized LyapunovKrasovskii functional techniques for investigating singular time-delay systems,Applied Mathematics Letters,24(2011)1152-1162.
[17]C.Peng,Y.C.Tian,Delay-dependent robust H∞control for uncertain systems with time-varying delay,Information Sciences,179(2009)3187-3197.
[18]S.Q.Zhu,C.H.Zhang,Z.L.Cheng,J.Feng,Delaydependent robust stability criteria for two classes of uncertain singular time-delay systems,IEEE Transactions on Automatic Control,52(2007)880-885.
[19]Z.Y.Liu,C.Lin,B.Chen,A neutral system approach to stability of singular time-delay systems,Journal of the Franklin Institute,351(2014)4939-4948.
[20]Z.Y.Liu,C.Lin,B.Chen,Admissibility analysis for linear singular systems with time-varying delays via neutral system approach,ISA Transactions,61(2016)141-146.
[21]M.Wu,Y.He,J.H.She,G.P.Liu,Delay-dependent criteria for robust stability of time-varying delay systems,Automatica,40(2004)1435-1439.
[22]Y.He,Q.G.Wang,L.Xie,C.Lin,Further improvement of free-weighting matrices technique for systems with timevarying delay,IEEE Transactions on Automatic Control,52(2007)293-299.
[23]K Gu,J.Chen,V.L.Kharitonov,Stability of time-delay systems,Springer Science,2003.
[24]A.Seuret,F.Gouaisbaut,Wirtinger-based integral inequality:Application to time-delay systems,Automatica,49(2013)2860-2866.
[25]H.B.Zeng,Y.He,M.Wu,J.H.She,Free-matrix-based integral inequality for stability analysis of systems with timevarying delay,IEEE Transactions on Automatic Control,60(2015)2768-2772.
[26]H.B.Zeng,Y.He,M.Wu,J.H.She,New results on stability analysis for systems with discrete distributed delay,Automatica,60(2015)189-192.
[27]Y.L.Zhi,Y.He,M.Wu,New stability criteria of singular systems with time-varying delay via free-matrix-based integral inequalities,Submitted to Applied Mathematics and Computation,2017.
[28]C.K.Zhang,Y.He,L.Jiang,M.Wu,H.B.Zeng,Stability analysis of systems with time-varying delay via relaxed integral inequalities,Systems and Control Letters,92(2016)52-61.
[29]P.G.Park,J.W.Ko,C.Jeong,Reciprocally convex approach to stability of systems with time-varying delays,Automatica,47(2011)235-238.
[2]S.Y.Xu,P.V.Dooren,R.Stefan,J.Lam,Robust stability and stabilization for singular delay systems with state delay and parameter uncertainty,IEEE Transactions on Automatic Control,47(2002)1122-1128.
[3]J.Chen,C.Lin,B.Chen,Q.G.Wang,Output feedback control for singular Markovian jump systems with uncertain transition rates,IET Control Theory and Applications,18(2016)2142-2147.
[4]C.Lin,J.Chen,B.Chen,L.Guo,Z.Zhang,Fuzzy nomalization and stabilization for a class of nonlinear rectangular descriptor systems,Neurocomputing,219(2017)263-268.
[5]L.V.Hien,L.H.Vu,V.N.Phat,Improved delay-dependent exponential stability of singular systems with mixed interval time-varying delays,IET Control Theory and Applications,9(2015)1364-1372.
[6]E.Fridman,Stability of linear descriptor systems with delay:a Lyapunov-based approach,Journal of Mathematical Analysis and Applications,273(2002)24-44.
[7]J.Chen,C.Lin,B.Chen,Q.G.Wang,Mixed H∞and passive control for singular systems with time delay via static output feedback,Applied Mathematics and Computation,293(2017)244-253.
[8]Z.G.Wu,J.H.Park,H.Su,J.Chu,Dissipativity analysis for singular systems with time-varying delays,Applied Mathematics and Computation,218(2011)4605-4613.
[9]H.Chen,P.Hu,New results on exponential stability for singular systems with two interval time-varying delays,IET Control Theory and Applications,15(2013)1941-1949.
[10]Z.Feng,W.Li,J.Lam,New admissibility analysis for discrete singular systems with time-varying delay,Applied Mathematics and Computation,265(2015)1058-1066.
[11]Z.G.Wu,J.H.Park,H.Su,J.Chu,Reliable passive control for singular systems with time-varying delays,Journal of Process Control,23(2013)1217-1228.
[12]X.L.Zhu,Y.Y.Wang,Y.Gan,H∞filtering for continuoustime singular systems with time-varying delay,International Journal of Adaptive Control and Signal Processing,25(2011)137-154.
[13]Y.Ariba,F.Gouaisbaut,An augmented model for robust stability analysis of time-varying delay systems,Internatinal Journal of Control,82(2009)1616-1626.
[14]M.J.Park,O.M.Kwon,J.H.Park,S.M.Lee,A new augmented Lyapunov-Krasovskii functional approach for stability of linear systems with time-varying delays,Applied Mathematics and Computation,217(2011)7197-7209.
[15]Y.He,Q.G.Wang,C.Lin,M.Wu,Augmented Lyapunov functional and delay-dependent stability criteria for neutral systems,International Journal of Robust and Nonlinear Control,15(2005)923-933.
[16]L.L.Liu,J.G.Peng,B.W.Wu,On parameterized LyapunovKrasovskii functional techniques for investigating singular time-delay systems,Applied Mathematics Letters,24(2011)1152-1162.
[17]C.Peng,Y.C.Tian,Delay-dependent robust H∞control for uncertain systems with time-varying delay,Information Sciences,179(2009)3187-3197.
[18]S.Q.Zhu,C.H.Zhang,Z.L.Cheng,J.Feng,Delaydependent robust stability criteria for two classes of uncertain singular time-delay systems,IEEE Transactions on Automatic Control,52(2007)880-885.
[19]Z.Y.Liu,C.Lin,B.Chen,A neutral system approach to stability of singular time-delay systems,Journal of the Franklin Institute,351(2014)4939-4948.
[20]Z.Y.Liu,C.Lin,B.Chen,Admissibility analysis for linear singular systems with time-varying delays via neutral system approach,ISA Transactions,61(2016)141-146.
[21]M.Wu,Y.He,J.H.She,G.P.Liu,Delay-dependent criteria for robust stability of time-varying delay systems,Automatica,40(2004)1435-1439.
[22]Y.He,Q.G.Wang,L.Xie,C.Lin,Further improvement of free-weighting matrices technique for systems with timevarying delay,IEEE Transactions on Automatic Control,52(2007)293-299.
[23]K Gu,J.Chen,V.L.Kharitonov,Stability of time-delay systems,Springer Science,2003.
[24]A.Seuret,F.Gouaisbaut,Wirtinger-based integral inequality:Application to time-delay systems,Automatica,49(2013)2860-2866.
[25]H.B.Zeng,Y.He,M.Wu,J.H.She,Free-matrix-based integral inequality for stability analysis of systems with timevarying delay,IEEE Transactions on Automatic Control,60(2015)2768-2772.
[26]H.B.Zeng,Y.He,M.Wu,J.H.She,New results on stability analysis for systems with discrete distributed delay,Automatica,60(2015)189-192.
[27]Y.L.Zhi,Y.He,M.Wu,New stability criteria of singular systems with time-varying delay via free-matrix-based integral inequalities,Submitted to Applied Mathematics and Computation,2017.
[28]C.K.Zhang,Y.He,L.Jiang,M.Wu,H.B.Zeng,Stability analysis of systems with time-varying delay via relaxed integral inequalities,Systems and Control Letters,92(2016)52-61.
[29]P.G.Park,J.W.Ko,C.Jeong,Reciprocally convex approach to stability of systems with time-varying delays,Automatica,47(2011)235-238.