H_∞ observer design for discrete-time singular systems with time-varying delay
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- 英文论文题名：H_∞ observer design for discrete-time singular systems with time-varying delay
- 论文作者：Yuxia Yang ; Chong Lin ; Bing Chen ; Jian Chen
- 英文论文作者：Yuxia Yang ; Chong Lin ; Bing Chen ; Jian Chen ; Institute of Complexity Science ; Qingdao University ; School of Science ; Qingdao University of Technology ; College of Automation Engineering ; Qingdao University of Technology
- 年：2017
- 作者机构：Institute of Complexity Science,Qingdao University;School of Science,Qingdao University of Technology;College of Automation Engineering,Qingdao University of Technology;
- 英文论文关键词：H_∞ observer design ; H_∞ performance ; Time-varying delay ; Discrete-time singular systems
- 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：207k
- 原文格式：D
- 会议级别：全国
摘要
This paper deals with the problem of H∞ full-order observer design for discrete-time linear singular systems with disturbance inputs and time-varying delay in state variables. A delay-dependent sufficient conditions is presented to guarantee the considered observer to be stable and satisfy the prescribed H∞ performance γ. The main procedure is based on LyapunovKrasovskii stability theory, where the optimal gain in the observer is a solution of linear matrix inequalities(LMIs). A numerical example is given to shown the effectiveness of the presented approach.
This paper deals with the problem of H_∞ full-order observer design for discrete-time linear singular systems with disturbance inputs and time-varying delay in state variables. A delay-dependent sufficient conditions is presented to guarantee the considered observer to be stable and satisfy the prescribed H_∞ performance γ. The main procedure is based on LyapunovKrasovskii stability theory, where the optimal gain in the observer is a solution of linear matrix inequalities(LMIs). A numerical example is given to shown the effectiveness of the presented approach.
This paper deals with the problem of H_∞ full-order observer design for discrete-time linear singular systems with disturbance inputs and time-varying delay in state variables. A delay-dependent sufficient conditions is presented to guarantee the considered observer to be stable and satisfy the prescribed H_∞ performance γ. The main procedure is based on LyapunovKrasovskii stability theory, where the optimal gain in the observer is a solution of linear matrix inequalities(LMIs). A numerical example is given to shown the effectiveness of the presented approach.
引文
[1]G.Verghese,B.Levy,and T.Kailath,A generalized state-space for singular systems,IEEE Trans.Autom.Control,4(26):811-831,1981.
[2]L.R.Fletcher,Regularizability of descriptor systems,International journal of systems science,17(6):843-847,1986.
[3]G.Duan,and Y.Chen,Generalized regularity and regularizability of rectangular descriptor systems,J.Control theory aoppl.,5(2):159-163,2007.
[4]K.Gu,V.L.Kharitonov,and J.Chen,Stability of Time-Delay Systems,Boston,MA,USA:Birkhuser,2003.
[5]Z.Wu,and W.Zhou,Delay-dependent robust H∞control for uncertain singular time-delay systems,IET Control Theory Applications,1:1234-1241,2007.
[6]Z.Feng,W.Li,and J.Lam,New admissibility analysis for discrete singular systems with time-varying delay,Applied Mathematics and Computation,265:1058-1066,Aug.2015.
[7]S.S.Delshad,and T.Gustafsson,Observer design for a class of nonlinear systems subject to unknown inputs,European Control Conferenc(ECC),June 24-27,in Strasbourg,France,316-319,2015.
[8]M.K.Gupta,and N.K.Tomar,and S.Bhaumik,Full-and reduced-order observer design for rectangular descriptor systems with unknown inputs,Journal of the Franklin Institute,352:1250-1264,2015.
[9]M.Khadhraoui,M.Ezzine,H.Messaoud,and M.Darouach,Design of full order unknown input observers for delayed singular systems with state variable time delay,IEEE.ISCCSP,624-627,2014.
[10]M.Khadhraoui,M.Ezzine,H.Messaoud,and M.Darouach,Functional observer design with unknown inputs for delayed singular systems:the discrete-time case,22nd Mediterranean Conferenc on Control and Automation,in Palermo,Italy,June16-19,127-132,2014.
[11]D.Koenig,S.Mammar,Design of proportional-integral observer for unknown input descriptor systems,IEEE Transations on Automatic Control,47(12):2057-2062,2002.
[12]D.Koenig,and B.Marx,Observer design with H∞performance for delay desccriptor systems,Proceedings of the2007 American Control Conference,Marriott Marquis Hotel at Times Square,New York City,USA,July 11-13,2007.
[13]A.Seurel,F.Gouaisbaut,and E.Fridman,Stability of discrete-time systems with time-Varying delays via a novel summation inequality,IEEE Transactions on Automatic Control,60(10):2740-2745,2015.[[[[[
[14]P.Park,W.I.Lee,and S.Y.Lee,Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems,Journal of The Franklin Institute,352:1378-1396,2015.
[15]S.Xu,P.V.Dooren,R.Stefan and J.Lam,Robust stability and stabilization for singular systems with state delay and parameter uncertainty,IEEE Transactions on Automatic Control,47(7):1122-1128,2002.
[16]S.Xu,and J.Lam,Improved delay-dependent stability criteria for time-delay systems,IEEE Transactions on Automatic Control,50(3):384-387,2005.
[17]S.Long,and S.Zhong,H∞control of a calss of discretetime singular systems via dynamic feedback controller,Applied Mathematics Letters,58:110-118,2016.
[18]S.Zhu,Z.Cheng,and F.June,Robust output feedback stabilization for uncertain singular time delay systems,Proceedings of the 2004 American Control Conference,Boston Massachusetts,USA,5416-5421,June,2004.
[19]H.Su,X.Ji,and J.Chu,Delay dependent robust control for uncertain singular time delay,Asian Journal of Control,8(2):180-189 2006.
[20]S.Zhu,C.Zhang,Z.Cheng,and J.Feng,Delay dependent robust stability criteria for two classes of uncertain singular time delay systems,IEEE Transations on Automatic Control,52(4):880-885,2007.
[21]D.Ma,Z.Cheng,C.Zhang,Delay-dependent robust stability and stabilisation for uncertain discrete singular systems with time-varying delays,IET Control Theory and Applications,1:1086-1095,2007.
[22]M.Darouach,M.Zasadzinski,M.Hayar,Reduced-order observer design for descriptor systems with time delays and unknown inputs,IEEE Transations on Automatic Control,41(7):1068-1072,1996.
[23]M.Darouach,L.Boutat-Baddas,M.Zasadzinski,H∞observers design for a class of nonlinear singular systems,Automatica,47(11):2517-2525,2011.
[24]J.Lin,Y.Shi,Z.Gao,and J.Ding,Funtional observer for switched discrete-time singular systems with time delays and unknown inputs,IET Control Theory and Applications,9(14):2146-2156,2015.
[25]M.K.Gupta,and N.K.Tomar,and S.Bhaumik,Observer design for descriptor systems with Lipschitz nonlinearities:an LMI approach,Nonlinear Dyn.syst.Theory,14(3):292-302,2014.
[2]L.R.Fletcher,Regularizability of descriptor systems,International journal of systems science,17(6):843-847,1986.
[3]G.Duan,and Y.Chen,Generalized regularity and regularizability of rectangular descriptor systems,J.Control theory aoppl.,5(2):159-163,2007.
[4]K.Gu,V.L.Kharitonov,and J.Chen,Stability of Time-Delay Systems,Boston,MA,USA:Birkhuser,2003.
[5]Z.Wu,and W.Zhou,Delay-dependent robust H∞control for uncertain singular time-delay systems,IET Control Theory Applications,1:1234-1241,2007.
[6]Z.Feng,W.Li,and J.Lam,New admissibility analysis for discrete singular systems with time-varying delay,Applied Mathematics and Computation,265:1058-1066,Aug.2015.
[7]S.S.Delshad,and T.Gustafsson,Observer design for a class of nonlinear systems subject to unknown inputs,European Control Conferenc(ECC),June 24-27,in Strasbourg,France,316-319,2015.
[8]M.K.Gupta,and N.K.Tomar,and S.Bhaumik,Full-and reduced-order observer design for rectangular descriptor systems with unknown inputs,Journal of the Franklin Institute,352:1250-1264,2015.
[9]M.Khadhraoui,M.Ezzine,H.Messaoud,and M.Darouach,Design of full order unknown input observers for delayed singular systems with state variable time delay,IEEE.ISCCSP,624-627,2014.
[10]M.Khadhraoui,M.Ezzine,H.Messaoud,and M.Darouach,Functional observer design with unknown inputs for delayed singular systems:the discrete-time case,22nd Mediterranean Conferenc on Control and Automation,in Palermo,Italy,June16-19,127-132,2014.
[11]D.Koenig,S.Mammar,Design of proportional-integral observer for unknown input descriptor systems,IEEE Transations on Automatic Control,47(12):2057-2062,2002.
[12]D.Koenig,and B.Marx,Observer design with H∞performance for delay desccriptor systems,Proceedings of the2007 American Control Conference,Marriott Marquis Hotel at Times Square,New York City,USA,July 11-13,2007.
[13]A.Seurel,F.Gouaisbaut,and E.Fridman,Stability of discrete-time systems with time-Varying delays via a novel summation inequality,IEEE Transactions on Automatic Control,60(10):2740-2745,2015.[[[[[
[14]P.Park,W.I.Lee,and S.Y.Lee,Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems,Journal of The Franklin Institute,352:1378-1396,2015.
[15]S.Xu,P.V.Dooren,R.Stefan and J.Lam,Robust stability and stabilization for singular systems with state delay and parameter uncertainty,IEEE Transactions on Automatic Control,47(7):1122-1128,2002.
[16]S.Xu,and J.Lam,Improved delay-dependent stability criteria for time-delay systems,IEEE Transactions on Automatic Control,50(3):384-387,2005.
[17]S.Long,and S.Zhong,H∞control of a calss of discretetime singular systems via dynamic feedback controller,Applied Mathematics Letters,58:110-118,2016.
[18]S.Zhu,Z.Cheng,and F.June,Robust output feedback stabilization for uncertain singular time delay systems,Proceedings of the 2004 American Control Conference,Boston Massachusetts,USA,5416-5421,June,2004.
[19]H.Su,X.Ji,and J.Chu,Delay dependent robust control for uncertain singular time delay,Asian Journal of Control,8(2):180-189 2006.
[20]S.Zhu,C.Zhang,Z.Cheng,and J.Feng,Delay dependent robust stability criteria for two classes of uncertain singular time delay systems,IEEE Transations on Automatic Control,52(4):880-885,2007.
[21]D.Ma,Z.Cheng,C.Zhang,Delay-dependent robust stability and stabilisation for uncertain discrete singular systems with time-varying delays,IET Control Theory and Applications,1:1086-1095,2007.
[22]M.Darouach,M.Zasadzinski,M.Hayar,Reduced-order observer design for descriptor systems with time delays and unknown inputs,IEEE Transations on Automatic Control,41(7):1068-1072,1996.
[23]M.Darouach,L.Boutat-Baddas,M.Zasadzinski,H∞observers design for a class of nonlinear singular systems,Automatica,47(11):2517-2525,2011.
[24]J.Lin,Y.Shi,Z.Gao,and J.Ding,Funtional observer for switched discrete-time singular systems with time delays and unknown inputs,IET Control Theory and Applications,9(14):2146-2156,2015.
[25]M.K.Gupta,and N.K.Tomar,and S.Bhaumik,Observer design for descriptor systems with Lipschitz nonlinearities:an LMI approach,Nonlinear Dyn.syst.Theory,14(3):292-302,2014.