Passivity and feedback passification of switched discrete-time linear systems

Abstract This paper focuses on the passivity analysis and feedback passification for switched discrete-time linear systems using multiple storage functions under a certain switching law. Controllers and switching laws are designed based on complete and partial state measurements, respectively. Conditions for strict passivity of a switched discrete-time system are obtained without the requirement of strict passivity of subsystems. In the case of partial state measurements, dynamic output feedback controllers for subsystems are designed, and a switching law depending only on the state of the output feedback controllers is constructed to guarantee strict passivity of the closed-loop switched system. Finally, a numerical example is provided to demonstrate the feasibility of the theoretical results.

[1]  D. Xie,et al.  Average dwell-time approach to L2 gain control synthesis of switched linear systems with time delay in detection of switching signal , 2009 .

[2]  Bin Jiang,et al.  Fault Tolerance Analysis for Switched Systems Via Global Passivity , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  Yan Shi,et al.  Dissipativity analysis and synthesis of a class of nonlinear systems with time-varying delays , 2009, J. Frankl. Inst..

[4]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[5]  David J. Hill,et al.  Decomposable Dissipativity and Related Stability for Discrete-Time Switched Systems , 2011, IEEE Transactions on Automatic Control.

[6]  Guo-Ping Liu,et al.  Delay-dependent stability for discrete systems with large delay sequence based on switching techniques , 2008, Autom..

[7]  Lihua Xie,et al.  Dissipative control for linear discrete-time systems , 1999, Autom..

[8]  Bin Jiang,et al.  On stabilization of switched nonlinear systems with unstable modes , 2009, Syst. Control. Lett..

[9]  Jun Zhao,et al.  Passivity and stability of switched systems: A multiple storage function method , 2008, Syst. Control. Lett..

[10]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[11]  Magdi S. Mahmoud,et al.  Passive control synthesis for uncertain systems with multiple-state delays , 2002, Comput. Electr. Eng..

[12]  R. Decarlo,et al.  Asymptotic Stability of m-Switched Systems using Lyapunov-Like Functions , 1991, 1991 American Control Conference.

[13]  Magdi S. Mahmoud,et al.  Switched Time-Delay Systems , 2010 .

[14]  Zhengrong Xiang,et al.  Robust reliable control for uncertain switched nonlinear systems with time delay , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[15]  P. Moylan,et al.  The stability of nonlinear dissipative systems , 1976 .

[16]  Mehrdad Saif,et al.  PASSIVITY AND PASSIVITY BASED CONTROLLER DESIGN OF A CLASS OF SWITCHED CONTROL SYSTEMS , 2005 .

[17]  Magdi S. Mahmoud.  Delay-dependent dissipativity analysis and synthesis of switched delay systems , 2011 .

[18]  Jun Zhao,et al.  Dissipativity Theory for Switched Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[19]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.

[20]  Jun Zhao,et al.  On stability, L2-gain and Hinfinity control for switched systems , 2008, Autom..

[21]  Magdi S. Mahmoud,et al.  Robust Stability and Stabilization of a Class of Nonlinear Switched Discrete-Time Systems with Time-Varying Delays , 2009 .

[22]  Bernhard Maschke,et al.  Dissipative Systems Analysis and Control , 2000 .

[23]  P.J. Antsaklis,et al.  Switching Stabilization and l2 Gain Performance Controller Synthesis for Discrete-Time Switched Linear Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[24]  A. Isidori,et al.  Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems , 1991 .

[25]  A. Schaft.  L2-Gain and Passivity Techniques in Nonlinear Control. Lecture Notes in Control and Information Sciences 218 , 1996 .

[26]  Jamal Daafouz,et al.  Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach , 2002, IEEE Trans. Autom. Control..

[27]  Leon O. Chua,et al.  Energy concepts in the state-space theory of nonlinear n-ports: Part I-Passivity , 1981 .

[28]  Panagiotis D. Christofides,et al.  Output feedback control of switched nonlinear systems using multiple Lyapunov functions , 2001, Proceedings of the 2005, American Control Conference, 2005..

[29]  C. Ahn.  Switched exponential state estimation of neural networks based on passivity theory , 2012 .

[30]  M. Zefran,et al.  A notion of passivity for hybrid systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[31]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[32]  Wen-an Zhang,et al.  Stability analysis for discrete-time switched time-delay systems , 2009, Autom..

[33]  A. Michel,et al.  Stability theory for hybrid dynamical systems , 1998, IEEE Trans. Autom. Control..

[34]  M. Jirstrand,et al.  On stability and passivity of a class of hybrid systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[35]  K. Hu,et al.  Improved robust H8 filtering for uncertain discrete-time switched systems , 2009 .

[36]  Patrizio Colaneri,et al.  Dynamic Output Feedback Control of Switched Linear Systems , 2008, IEEE Transactions on Automatic Control.

[37]  M. Mahmoud,et al.  Passivity and passification of time-delay systems , 2004 .

[38]  P. Moylan,et al.  Dissipative Dynamical Systems: Basic Input-Output and State Properties , 1980 .

[39]  Alberto Bemporad,et al.  Passivity Analysis and Passification of Discrete-Time Hybrid Systems , 2008, IEEE Transactions on Automatic Control.

[40]  Xi-Ming Sun,et al.  Stability analysis for networked control systems based on average dwell time method , 2010 .

[41]  Ilia G. Polushin,et al.  On the existence of a continuous storage function for dissipative systems , 2002, Syst. Control. Lett..

[42]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

[43]  Patrizio Colaneri,et al.  Passivity of switched linear systems: Analysis and control design , 2012, Syst. Control. Lett..

[44]  Huaguang Zhang,et al.  Stabilization of Switched Nonlinear Systems With All Unstable Modes: Application to Multi-Agent Systems , 2011, IEEE Transactions on Automatic Control.