Strict Passivity and feedback passification of Switched Discrete-time Affine Nonlinear Systems Using Linearization
详细信息 查看官网全文
- 英文论文题名：Strict Passivity and feedback passification of Switched Discrete-time Affine Nonlinear Systems Using Linearization
- 论文作者：Hanmei Wang ; Jun Zhao
- 英文论文作者：Hanmei Wang ; Jun Zhao ; State Key Laboratory of Synthetical Automation for Process Industries (Northeastern University) ; College of Information Science and Engineering ; Northeastern University ; College of Mathematics and Information Science ; Shangqiu Normal University
- 年：2017
- 作者机构：State Key Laboratory of Synthetical Automation for Process Industries (Northeastern University),College of Information Science and Engineering,Northeastern University;College of Mathematics and Information Science,Shangqiu Normal University;
- 英文论文关键词：Switched discrete-time affine nonlinear system ; strict passivity ; feedback passification ; linearization ; dwell-time dependent storage function
- 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：TP273
- 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：268k
- 原文格式：D
- 会议级别：全国
摘要
In this paper, local strict passivity of a switched discrete-time affine nonlinear system is investigated using the linearization technique. The dwell-time dependent storage function(DTDSF) is employed to analyze passivity and solve feedback passification problem. First, local strict passivity sufficient conditions are established in terms of LMIs, which are all convex in linearized system matrices. And then, feedback passification of a switched discrete-time affine nonlinear system is addressed when the dynamic system is not strictly passive. A numerical example is given to illustrate that controller design and switching law design can lumped into a unified design step to make a non-passivity switched system passive.
In this paper, local strict passivity of a switched discrete-time affine nonlinear system is investigated using the linearization technique. The dwell-time dependent storage function(DTDSF) is employed to analyze passivity and solve feedback passification problem. First, local strict passivity sufficient conditions are established in terms of LMIs, which are all convex in linearized system matrices. And then, feedback passification of a switched discrete-time affine nonlinear system is addressed when the dynamic system is not strictly passive. A numerical example is given to illustrate that controller design and switching law design can lumped into a unified design step to make a non-passivity switched system passive.
In this paper, local strict passivity of a switched discrete-time affine nonlinear system is investigated using the linearization technique. The dwell-time dependent storage function(DTDSF) is employed to analyze passivity and solve feedback passification problem. First, local strict passivity sufficient conditions are established in terms of LMIs, which are all convex in linearized system matrices. And then, feedback passification of a switched discrete-time affine nonlinear system is addressed when the dynamic system is not strictly passive. A numerical example is given to illustrate that controller design and switching law design can lumped into a unified design step to make a non-passivity switched system passive.
引文
[1]S.Huang,and Z.Xiang,Finite-time stabilization of switched stochastic nonlinear systems with mixed odd and even powers,Automatica,73:130–137(2016).
[2]R.Ma,J.Zhao,Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings,Automatica,46(11):1819–1823(2010).
[3]Y.Wang,X.Sun,and F.Mazenc,Stability of switched nonlinear systems with delay and disturbance.Automatica,69:78–86(2016).
[4]J.Fu,T.Li,T.Chai,and C.Su,Sampled-data-based stabilization of switched linear neutral systems,Automatica,72:92–99(2016).
[5]J.Zhao,and D.Hill,On stability,L2 gain and H∞control for switched systems,Automatica,44(5):1220–1232(2008).
[6]N.H.El-Farra,P.D.Christofides,Output feedback control of switched nonlinear systems using multiple Lyapunov functions,Syst.Control Lett.,54(12):1163–1182(2005).
[7]W.Ren,and J.Xiong,Stability and stabilization of switched stochastic systems under asynchronous switching,Syst.Control Lett.,97:184–192,(2016).
[8]J.Xiong J.Lam Z.Shu X.Mao,Stability analysis of continuoustime switched systems with a random switching signal,IEEE Trans.Autom.Control,59(1):180–186(2013).
[9]L.Allerhand,and U.Shaked,Robust state-dependent switching of linear systems with dwell time,IEEE Trans.Autom.Control,58(4):994–1001(2013).
[10]J.S.Kim,T.W.Yoon,C.De Persis,Discrete-time supervisory control of input-constrained neutrally stable linear systems via state-dependent dwell-time switching,Syst.Control Lett.,56(7–8):484–49(2007).
[11]W.Lin,C.Byrnes,KYP lemma,state feedback and dynamic output feedback in discrete-time bilinear systems,Syst.Control Lett.,23(2):127-136(1994).
[12]M.Zefran,F.Bullo and M.Stein,A notion of passivity for hybrid systems,in Proc.40th IEEE Conf.Decis.Control,1:768–773(2001).
[13]J.Zhao,and D.Hill,A notion of passivity for switched systems with state-dependent switching.J.Control Theory Applicat.,4(1):70–75(2006).
[14]J.Zhao,and D.Hill,Dissipativity theory for switched systems,IEEE Trans.Automat.Control 53:941–953(2008).
[15]W.Haddad,T.Sadikhov,Dissipative differential inclusions,set-valued energy storage and supply rate maps,and stability of discontinuous feedback systems,Nonlinear Anal.Hybrid Syst.,8:83–108(2013).
[16]R.Sakthivel,T.Saravanakumar,B.Kaviarasan,and S.Marshal Anthoni,Dissipativity based repetitive control for switched stochastic dynamical systems,Appl.Math.Comput.,291:340–353(2016).
[17]A.Ruiz,A.van der Schaft,On passivity systems:From linearity to nonlinearity,in Proc.2nd IFAC Symp.Nonlinear Control Systems(NOLCOS 2004),373–378(1993).
[18]M.Xia,P.J.Antsaklis,V.Gupta,and M.J.Mc Court,Determining passivity using linearization for systems with feedthrough terms,IEEE Trans.Automat.Control,60(9):2536–2541(2015).
[19]M.Xia,P.J.Antsaklis,V.Gupta and F.Zhu,Passivity and dissipativity analysis of a system and its approximation,IEEE Trans.Automat.Control,PP(99):1–1(2016).
[20]W.Xiang,J.Xiao and G.Zhai,Dissipativity and dwell-time specifications of switched discrete-time systems and its applications in H∞and robust passive control,Inform.Sci.,320:206–222(2015).
[21]Y.Wang,V.Gupta,and P.J.Antsaklis,On passivity of a class of discrete-time switched nonlinear systems.IEEE Trans.Automat.Control,59(3):629–702(2014).
[2]R.Ma,J.Zhao,Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings,Automatica,46(11):1819–1823(2010).
[3]Y.Wang,X.Sun,and F.Mazenc,Stability of switched nonlinear systems with delay and disturbance.Automatica,69:78–86(2016).
[4]J.Fu,T.Li,T.Chai,and C.Su,Sampled-data-based stabilization of switched linear neutral systems,Automatica,72:92–99(2016).
[5]J.Zhao,and D.Hill,On stability,L2 gain and H∞control for switched systems,Automatica,44(5):1220–1232(2008).
[6]N.H.El-Farra,P.D.Christofides,Output feedback control of switched nonlinear systems using multiple Lyapunov functions,Syst.Control Lett.,54(12):1163–1182(2005).
[7]W.Ren,and J.Xiong,Stability and stabilization of switched stochastic systems under asynchronous switching,Syst.Control Lett.,97:184–192,(2016).
[8]J.Xiong J.Lam Z.Shu X.Mao,Stability analysis of continuoustime switched systems with a random switching signal,IEEE Trans.Autom.Control,59(1):180–186(2013).
[9]L.Allerhand,and U.Shaked,Robust state-dependent switching of linear systems with dwell time,IEEE Trans.Autom.Control,58(4):994–1001(2013).
[10]J.S.Kim,T.W.Yoon,C.De Persis,Discrete-time supervisory control of input-constrained neutrally stable linear systems via state-dependent dwell-time switching,Syst.Control Lett.,56(7–8):484–49(2007).
[11]W.Lin,C.Byrnes,KYP lemma,state feedback and dynamic output feedback in discrete-time bilinear systems,Syst.Control Lett.,23(2):127-136(1994).
[12]M.Zefran,F.Bullo and M.Stein,A notion of passivity for hybrid systems,in Proc.40th IEEE Conf.Decis.Control,1:768–773(2001).
[13]J.Zhao,and D.Hill,A notion of passivity for switched systems with state-dependent switching.J.Control Theory Applicat.,4(1):70–75(2006).
[14]J.Zhao,and D.Hill,Dissipativity theory for switched systems,IEEE Trans.Automat.Control 53:941–953(2008).
[15]W.Haddad,T.Sadikhov,Dissipative differential inclusions,set-valued energy storage and supply rate maps,and stability of discontinuous feedback systems,Nonlinear Anal.Hybrid Syst.,8:83–108(2013).
[16]R.Sakthivel,T.Saravanakumar,B.Kaviarasan,and S.Marshal Anthoni,Dissipativity based repetitive control for switched stochastic dynamical systems,Appl.Math.Comput.,291:340–353(2016).
[17]A.Ruiz,A.van der Schaft,On passivity systems:From linearity to nonlinearity,in Proc.2nd IFAC Symp.Nonlinear Control Systems(NOLCOS 2004),373–378(1993).
[18]M.Xia,P.J.Antsaklis,V.Gupta,and M.J.Mc Court,Determining passivity using linearization for systems with feedthrough terms,IEEE Trans.Automat.Control,60(9):2536–2541(2015).
[19]M.Xia,P.J.Antsaklis,V.Gupta and F.Zhu,Passivity and dissipativity analysis of a system and its approximation,IEEE Trans.Automat.Control,PP(99):1–1(2016).
[20]W.Xiang,J.Xiao and G.Zhai,Dissipativity and dwell-time specifications of switched discrete-time systems and its applications in H∞and robust passive control,Inform.Sci.,320:206–222(2015).
[21]Y.Wang,V.Gupta,and P.J.Antsaklis,On passivity of a class of discrete-time switched nonlinear systems.IEEE Trans.Automat.Control,59(3):629–702(2014).