Stability Analysis for a Class of Time-varying Delay Linear Systems Based on Delay Decomposition Method
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- 英文论文题名：Stability Analysis for a Class of Time-varying Delay Linear Systems Based on Delay Decomposition Method
- 论文作者：Huaxu Fan ; Xiefu Jiang ; Chaochao Tang ; Zixiang Guo
- 英文论文作者：Huaxu Fan ; Xiefu Jiang ; Chaochao Tang ; Zixiang Guo ; School of Automation ; Hangzhou Dianzi University
- 年：2017
- 作者机构：School of Automation,Hangzhou Dianzi University;
- 英文论文关键词：time-varying delay ; delay decomposition method ; stability criterion ; linear matrix inequalities
- 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;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：139k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, we consider the stability of a class of linear systems with a time-varying delay. By using delay decomposition method, the time-delay interval is decomposed into two sub intervals to construct a suitable Lyapunov-Krasovskii functional, and each term of the Lyapunov-Krasovskii functional do not need to be positive definite, the partial items of Lyapunov-Krasovskii functional are consider that as a whole to determine its positive definiteness. And then different integral terms obtained in Lyapunov-Krasovskii functional derivatives are treated separately by using specific integral inequality, convex combination principle and Jensen's inequality, respectively. Next, an improved stability criterion for a class of linear systems with a time-varying delay is given in the term of linear matrix inequalities(LMIs). Finally, an example is given to show the effectiveness of the proposed method.
In this paper, we consider the stability of a class of linear systems with a time-varying delay. By using delay decomposition method, the time-delay interval is decomposed into two sub intervals to construct a suitable Lyapunov-Krasovskii functional, and each term of the Lyapunov-Krasovskii functional do not need to be positive definite, the partial items of Lyapunov-Krasovskii functional are consider that as a whole to determine its positive definiteness. And then different integral terms obtained in Lyapunov-Krasovskii functional derivatives are treated separately by using specific integral inequality, convex combination principle and Jensen's inequality, respectively. Next, an improved stability criterion for a class of linear systems with a time-varying delay is given in the term of linear matrix inequalities(LMIs). Finally, an example is given to show the effectiveness of the proposed method.
In this paper, we consider the stability of a class of linear systems with a time-varying delay. By using delay decomposition method, the time-delay interval is decomposed into two sub intervals to construct a suitable Lyapunov-Krasovskii functional, and each term of the Lyapunov-Krasovskii functional do not need to be positive definite, the partial items of Lyapunov-Krasovskii functional are consider that as a whole to determine its positive definiteness. And then different integral terms obtained in Lyapunov-Krasovskii functional derivatives are treated separately by using specific integral inequality, convex combination principle and Jensen's inequality, respectively. Next, an improved stability criterion for a class of linear systems with a time-varying delay is given in the term of linear matrix inequalities(LMIs). Finally, an example is given to show the effectiveness of the proposed method.
引文
[1]J.P.Richard,Time-delay systems:an overview of some recent advances and open problems,Automatica,39(10):1667-1694,2003.
[2]O.M.Kwon,M.J.Park,S.M.Lee,Augmented LyapunovKrasovskii functional approaches to robust stability criteria for uncertain Takagi-Sugeno fuzzy systems with time-varying delays,Fuzzy Sets and Systems,201(1):1-19,2012.
[3]M.Wu,Y.He,J.H.She,Delay-dependent criteria for robust stability of time-varying delay systems,Automatica,40(8):1435-1439,2004.
[4]C.Y.Kao,B.Lincoln,Simple stability criteria for systems with time-varying delays,Automatica,40(8):1429-1434,2004.
[5]W.I.Lee,S.Y.Lee,P.Park,Improved criteria on robust stability and performance for linear systems with interval time-varying delays via new triple integral functionals,Applied Mathematics and Computation,243(1):570-577,2014.
[6]O.M.Kwon,M.J.Park,J.H.Park,Analysis on robust∞H performance and stability for linear systems with interval time-varying state delays via some new augmented Lyapunov-K-rasovskii functional,Applied Mathematics and Computation,224(0):108-122,2013.
[7]C.Jeong,P.Park,S.H.Kim,Improved approach to robust stability and∞H performance analysis for systems with an interval time-varying delay,Applied Mathematics and Computation,218(21):10533-10541,2012.
[8]D.Yue,Q.L.Han,J.Lam,Network-based robust∞H control of systems with uncertainty,Automatica,41(6):999-1007,2005.
[9]J.Kim,Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty,IEEE Trans Automatic Control,46(5):789-792,2001.
[10]D.Yue,Robust stabilization of uncertain systems with unknown input delay,Automatica,40(2):331-336,2004.
[11]L.D.Guo,X.Q.He,J.J.He,New delay-decomposing approaches to stability criteria for delayed neural networks,Neurocomputing,189(0):123-129,2016.
[12]S.Senthilraj,R.Raja,Q.X.Zhu,New delay-interval-dependent stability criteria for static neural networks with time-varying delays,Neurocomputing,186(0):1-7,2016.
[13]Y.J.Liu,S.M.Lee,O.M.Kwon,New approach to stability criteria for generalized neural networks with interval time-varying delays,Neurocomputing,149(C):1544-1551,2015.
[14]P.Park,J.W.Ko,C.Jeong,Reciprocally convex approach to stability of systems with time-varying delays,Automatica,47(1):235-238,2011.
[15]X.J.Jing,D.L.Tan,Y.C.Wang,An LMI approach to stability of systems with severe time-delay,IEEE Trans.on Automatic Control,49(7):1192-1195,2004.
[16]S.Xu,J.Lam,Y.Zou,Simplified descriptor system approach to delay-dependent stability and performance analyses for time-delay systems,IEEE Proceedings-Control Theory and Applications,152(2):147-151,2005.
[17]F.Gouaisbaut,D.Peaucelle,Delay-dependent robust stability of time delay systems,International Journal of Ecology and Development,183(2):980-989,2006.
[18]L.James,H.J.Gao,C.H.Wang,Stability analysis for continuous systems with two additive time-varying delay components,Systems and Control Letters,56(1):16-24,2007.
[19]H.Gao,T.Chen,J.Lam,A new delay systems approach to network-based control,Automatica,44(1):39-52,2008.
[20]W.Qian,T.Li,S.Cong,Stability analysis for interval timevarying delay systems based on time-varying bound integral method,Journal of the Franklin Institute,351(1):4892-4903,2014.
[21]Q.L.Han,Absolute stability of time-delay systems with sector bounded nonlinearity,Automatica,41(12):2171-2176,2005.
[22]J.Lam,H.Gao,C.Wang,Stability analysis for continuous systems with two additive time-varying delay component,System&Control Letter,56(1):16-24,2007.
[23]P.L.Liu,Further resuits on delay-range-dependent stability with additive time-varying delay systems,ISA Transactions,53(2):258-266,2014.
[24]H.Y.Shao,Z.Q.Zhang,Control for a networked control model of systems with two additive time-varying delays,Abstract and Applied Analysisl,0(0):1-9,2014.
[25]X.H.Ge,Comments and an improved result on“Stability analysis for continuous system with additive time-varying delays:A less conservative result”,Applied Mathematics and Computation,241(15):42-46,2014.
[26]X.M.Yu,X.M.Wang,S.M.Zhong,Further results on delay-dependent stability for continuous system with two additive time-varying delay components,ISA Iransactions,65:9-18,2016.
[27]H.Y.Shao,Z.Q.Zhang,Delay-dependent state feedback stabilization for a networked control model with two additive input delays,Applied Mathematics and Computation,265:748-758,2015.
[2]O.M.Kwon,M.J.Park,S.M.Lee,Augmented LyapunovKrasovskii functional approaches to robust stability criteria for uncertain Takagi-Sugeno fuzzy systems with time-varying delays,Fuzzy Sets and Systems,201(1):1-19,2012.
[3]M.Wu,Y.He,J.H.She,Delay-dependent criteria for robust stability of time-varying delay systems,Automatica,40(8):1435-1439,2004.
[4]C.Y.Kao,B.Lincoln,Simple stability criteria for systems with time-varying delays,Automatica,40(8):1429-1434,2004.
[5]W.I.Lee,S.Y.Lee,P.Park,Improved criteria on robust stability and performance for linear systems with interval time-varying delays via new triple integral functionals,Applied Mathematics and Computation,243(1):570-577,2014.
[6]O.M.Kwon,M.J.Park,J.H.Park,Analysis on robust∞H performance and stability for linear systems with interval time-varying state delays via some new augmented Lyapunov-K-rasovskii functional,Applied Mathematics and Computation,224(0):108-122,2013.
[7]C.Jeong,P.Park,S.H.Kim,Improved approach to robust stability and∞H performance analysis for systems with an interval time-varying delay,Applied Mathematics and Computation,218(21):10533-10541,2012.
[8]D.Yue,Q.L.Han,J.Lam,Network-based robust∞H control of systems with uncertainty,Automatica,41(6):999-1007,2005.
[9]J.Kim,Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty,IEEE Trans Automatic Control,46(5):789-792,2001.
[10]D.Yue,Robust stabilization of uncertain systems with unknown input delay,Automatica,40(2):331-336,2004.
[11]L.D.Guo,X.Q.He,J.J.He,New delay-decomposing approaches to stability criteria for delayed neural networks,Neurocomputing,189(0):123-129,2016.
[12]S.Senthilraj,R.Raja,Q.X.Zhu,New delay-interval-dependent stability criteria for static neural networks with time-varying delays,Neurocomputing,186(0):1-7,2016.
[13]Y.J.Liu,S.M.Lee,O.M.Kwon,New approach to stability criteria for generalized neural networks with interval time-varying delays,Neurocomputing,149(C):1544-1551,2015.
[14]P.Park,J.W.Ko,C.Jeong,Reciprocally convex approach to stability of systems with time-varying delays,Automatica,47(1):235-238,2011.
[15]X.J.Jing,D.L.Tan,Y.C.Wang,An LMI approach to stability of systems with severe time-delay,IEEE Trans.on Automatic Control,49(7):1192-1195,2004.
[16]S.Xu,J.Lam,Y.Zou,Simplified descriptor system approach to delay-dependent stability and performance analyses for time-delay systems,IEEE Proceedings-Control Theory and Applications,152(2):147-151,2005.
[17]F.Gouaisbaut,D.Peaucelle,Delay-dependent robust stability of time delay systems,International Journal of Ecology and Development,183(2):980-989,2006.
[18]L.James,H.J.Gao,C.H.Wang,Stability analysis for continuous systems with two additive time-varying delay components,Systems and Control Letters,56(1):16-24,2007.
[19]H.Gao,T.Chen,J.Lam,A new delay systems approach to network-based control,Automatica,44(1):39-52,2008.
[20]W.Qian,T.Li,S.Cong,Stability analysis for interval timevarying delay systems based on time-varying bound integral method,Journal of the Franklin Institute,351(1):4892-4903,2014.
[21]Q.L.Han,Absolute stability of time-delay systems with sector bounded nonlinearity,Automatica,41(12):2171-2176,2005.
[22]J.Lam,H.Gao,C.Wang,Stability analysis for continuous systems with two additive time-varying delay component,System&Control Letter,56(1):16-24,2007.
[23]P.L.Liu,Further resuits on delay-range-dependent stability with additive time-varying delay systems,ISA Transactions,53(2):258-266,2014.
[24]H.Y.Shao,Z.Q.Zhang,Control for a networked control model of systems with two additive time-varying delays,Abstract and Applied Analysisl,0(0):1-9,2014.
[25]X.H.Ge,Comments and an improved result on“Stability analysis for continuous system with additive time-varying delays:A less conservative result”,Applied Mathematics and Computation,241(15):42-46,2014.
[26]X.M.Yu,X.M.Wang,S.M.Zhong,Further results on delay-dependent stability for continuous system with two additive time-varying delay components,ISA Iransactions,65:9-18,2016.
[27]H.Y.Shao,Z.Q.Zhang,Delay-dependent state feedback stabilization for a networked control model with two additive input delays,Applied Mathematics and Computation,265:748-758,2015.