Decentralized stabilization of interconnected switched descriptors via a multiple switched Lyapunov functional

Abstract The decentralized stabilization of large scale switched descriptor systems under arbitrary switching laws is proposed in this paper. A large scale switched descriptor can be split into a set of smaller interconnected switched descriptors. Then, a set of switched controllers is employed to ensure the stabilization of the considered class of large scale descriptors. The proposed LMI stability conditions are obtained from a multiple switched Lyapunov-like candidate function. A numerical example is given to illustrate the effectiveness of the designed approach.

[1]  Dalel Jabri,et al.  Decentralized Static Output Feedback control of interconnected fuzzy descriptors , 2010, 2010 IEEE International Symposium on Intelligent Control.

[2]  Dalel Jabri,et al.  Decentralized stabilization of discrete-time large scale switched systems , 2010, 18th Mediterranean Conference on Control and Automation, MED'10.

[3]  Long Wang,et al.  Linear matrix inequality approach to quadratic stabilisation of switched systems , 2004 .

[4]  Hiroaki Mukaidani,et al.  A numerical analysis of the Nash strategy for weakly coupled large-scale systems , 2006, IEEE Transactions on Automatic Control.

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

[6]  Bart De Schutter,et al.  Stabilization of switched affine systems: An application to the buck-boost converter , 2007, 2007 American Control Conference.

[7]  Kevin Guelton,et al.  Robust pole placement controller design in LMI region for uncertain and disturbed switched systems , 2008 .

[8]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

[9]  Magdi S. Mahmoud,et al.  Interconnected continuous-time switched systems: Robust stability and stabilization , 2010 .

[10]  Daniel Liberzon,et al.  On stability of linear switched differential algebraic equations , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[11]  Peng Shi,et al.  Stabilization of Linear Switched Delay Systems: ℋ2 and ℋ∞ Methods , 2009, J. Optimization Theory and Applications.

[12]  Mikael Johansson,et al.  Piecewise linear control systems - a computational approach , 2002, Lecture notes in control and information sciences.

[13]  D. Cobb,et al.  Descriptor variable systems and optimal state regulation , 1983 .

[14]  K. Guelton,et al.  Decentralized Stabilization of Continuous Time Large Scale Switched Descriptors , 2011 .

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

[16]  J. Chiou,et al.  Stability analysis for a class of switched large-scale time-delay systems via time-switched method , 2006 .

[17]  Srdjan S. Stankovic,et al.  Decentralized dynamic output feedback for robust stabilization of a class of nonlinear interconnected systems , 2007, Autom..

[18]  Jun Zhao,et al.  Control Lyapunov functions for switched control systems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[19]  P. Khargonekar,et al.  Robust stabilization of linear systems with norm-bounded time-varying uncertainty , 1988 .

[20]  G Chesi,et al.  Computing upper-bounds of the minimum dwell time of linear switched systems via homogeneous polynomial Lyapunov functions , 2010, Proceedings of the 2010 American Control Conference.

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

[22]  Michael Athans,et al.  Survey of decentralized control methods for large scale systems , 1978 .

[23]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[24]  M. Branicky.  Stability of hybrid systems: state of the art , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[25]  S. van Mourik,et al.  Switching input controller for a food storage room , 2010 .

[26]  Guisheng Zhai,et al.  A unified approach to stability analysis of switched linear descriptor systems under arbitrary switching , 2010, Int. J. Appl. Math. Comput. Sci..

[27]  Guisheng Zhai,et al.  A unified approach to analysis of switched linear descriptor systems under arbitrary switching , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.