Decentralized control of large scale switched Takagi-Sugeno systems

This paper deals with decentralized stabilization of large scale switched nonlinear systems under arbitrary switching laws. A global large scale switched system can be split into a set of smaller interconnected switched Takagi Sugeno fuzzy subsystems. Then, in order to stabilize the overall closed-loop system, a set of switched non-PDC controllers is employed. The latter is designed based on Linear Matrix Inequalities (LMI) conditions obtained from a multiple switched non quadratic like-Lyapunov candidate function. A numerical example is proposed to illustrate the effectiveness of the suggested decentralized switched controller design approach.

[1]  Guang Ren,et al.  Fuzzy Switching Controller for Multiple Model , 2005, FSKD.

[2]  Guisheng Zhai,et al.  A Note on Multiple Lyapunov Functions and Stability Condition for Switched and Hybrid Systems , 2007, 2007 IEEE International Conference on Control Applications.

[3]  Sangchul Won,et al.  A new fuzzy Lyapunov function approach for a Takagi-Sugeno fuzzy control system design , 2006, Fuzzy Sets Syst..

[4]  M. G. Karunambigai,et al.  A study on atanassov's intuitionistic fuzzy graphs , 2011, 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011).

[5]  Kevin Guelton,et al.  Stabilisation non quadratique locale pour des modèles continus de type Takagi-Sugeno , 2010 .

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

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

[8]  Dalel Jabri,et al.  Fuzzy Lyapunov decentralized control of Takagi-Sugeno interconnected descriptors , 2009, 2009 IEEE Symposium on Computational Intelligence in Control and Automation.

[9]  S. Begum Degree, Order and Size in Intuitionistic Fuzzy Graphs , 2010 .

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

[11]  Krassimir T. Atanassov,et al.  Operations on intuitionistic fuzzy graphs , 2009, 2009 IEEE International Conference on Fuzzy Systems.

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

[13]  Zhengrong Xiang,et al.  Control of switched systems with actuator saturation , 2006 .

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

[15]  A. Gani,et al.  Isomorphism on Fuzzy Graphs , 2008 .

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

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

[18]  Vesna M. Ojleska,et al.  Switched Fuzzy Systems: Overview and Perspectives , 2008 .

[19]  M. S. Mahmoud,et al.  Stabilization of Linear Switched Delay Systems : H 2 and H ∞ Methods , 2022 .

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

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

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

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

[24]  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).

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

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

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

[28]  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.

[29]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

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

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

[32]  Kazuo Tanaka,et al.  A multiple Lyapunov function approach to stabilization of fuzzy control systems , 2003, IEEE Trans. Fuzzy Syst..

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

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

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

[36]  Fernando de Oliveira Souza,et al.  Reducing conservativeness in recent stability conditions of TS fuzzy systems , 2009, Autom..

[37]  Igor Skrjanc,et al.  Fuzzy-model-based hybrid predictive control. , 2009, ISA transactions.