Decentralized control design for switched fuzzy large-scale systems with H∞ performance

This paper investigates the H ∞ control design problem for a class of switched discrete-time Takagi-Sugeno (T-S) fuzzy large-scale systems. The considered fuzzy large-scale systems consist of several interconnected subsystems with different switching modes and each switching mode is described by T-S fuzzy models. In addition, there exists the asynchronous switching between the system switching modes and the controller switching modes. By using parallel distributed compensation design method, a state feedback decentralized controller with H ∞ performance is developed. The sufficient conditions of ensuring the switched control system stability are proposed based on the theory of Lyapunov function and average-dwell time methods, which are formulated in the form of linear matrix inequalities (LMIs). An illustrated numerical example is provided to show the effectiveness of the obtained theoretical results.

[1]  Yongduan Song,et al.  A novel approach to output feedback control of fuzzy stochastic systems , 2014, Autom..

[2]  Shengyuan Xu,et al.  The Exponential Stability and Asynchronous Stabilization of a Class of Switched Nonlinear System Via the T–S Fuzzy Model , 2014, IEEE Transactions on Fuzzy Systems.

[3]  James Lam,et al.  Stability and Synchronization of Discrete-Time Neural Networks With Switching Parameters and Time-Varying Delays , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[4]  Xiaozhan Yang,et al.  Dissipativity Analysis and Synthesis for Discrete-Time T–S Fuzzy Stochastic SystemsWith Time-Varying Delay , 2014, IEEE Transactions on Fuzzy Systems.

[5]  Xiaofeng Liao,et al.  Stability analysis and H/sub /spl infin// controller design of fuzzy large-scale systems based on piecewise Lyapunov functions , 2005 .

[6]  G. Feng,et al.  A Survey on Analysis and Design of Model-Based Fuzzy Control Systems , 2006, IEEE Transactions on Fuzzy Systems.

[7]  Huijun Gao,et al.  Asynchronously switched control of switched linear systems with average dwell time , 2010, Autom..

[8]  Jun Zhao,et al.  Stability of dynamical networks with non-identical nodes: A multiple v-Lyapunov function method , 2011, Autom..

[9]  Kazuo Tanaka,et al.  Relaxed Stabilization Criterion for T–S Fuzzy Systems by Minimum-Type Piecewise-Lyapunov-Function-Based Switching Fuzzy Controller , 2012, IEEE Transactions on Fuzzy Systems.

[10]  Ligang Wu,et al.  Average dwell time approach to L 2 -L∞1 control of switched delay systems via dynamic output feedback , 2009 .

[11]  Zengqi Sun,et al.  Study on separation principles for T-S fuzzy system with switching controller and switching observer , 2010, Neurocomputing.

[12]  Kazuo Tanaka,et al.  Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

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

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

[15]  Y.-J. Chen,et al.  Relaxed Stabilization Criteria for Discrete-Time T–S Fuzzy Control Systems Based on a Switching Fuzzy Model and Piecewise Lyapunov Function , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[16]  Huijun Gao,et al.  Fault-tolerant control of Markovian jump stochastic systems via the augmented sliding mode observer approach , 2014, Autom..

[17]  Honghai Liu,et al.  Stability Analysis of Polynomial-Fuzzy-Model-Based Control Systems Using Switching Polynomial Lyapunov Function , 2013, IEEE Transactions on Fuzzy Systems.

[18]  Hamid Reza Karimi,et al.  Output-Feedback-Based $H_{\infty}$ Control for Vehicle Suspension Systems With Control Delay , 2014, IEEE Transactions on Industrial Electronics.

[19]  E. Boukas,et al.  Exponential H∞ filtering for uncertain discrete‐time switched linear systems with average dwell time: A µ‐dependent approach , 2008 .

[20]  Guang-Hong Yang,et al.  Switching Fuzzy Dynamic Output Feedback $H_{\infty}$ Control for Nonlinear Systems , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[21]  Gang Feng,et al.  Stability Analysis and $H_{\infty}$ Controller Design of Discrete-Time Fuzzy Large-Scale Systems Based on Piecewise Lyapunov Functions , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[22]  Ximing Sun,et al.  STABILIZATION AND SWITCHED CONTROL FOR A CLASS OF SWITCHED FUZZY SYSTEMS , 2009 .

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

[24]  Ligang Wu,et al.  A New Approach to Stability Analysis and Stabilization of Discrete-Time T-S Fuzzy Time-Varying Delay Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[25]  Hak-Keung Lam,et al.  Fuzzy Sampled-Data Control for Uncertain Vehicle Suspension Systems , 2014, IEEE Transactions on Cybernetics.

[26]  Peng Shi,et al.  $l_{2}-l_{\infty}$ Model Reduction for Switched LPV Systems With Average Dwell Time , 2008, IEEE Transactions on Automatic Control.

[27]  Xiaofeng Liao,et al.  Stability analysis and H infinity controller design of fuzzy large-scale systems based on piecewise Lyapunov functions. , 2006, IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society.

[28]  A. Michel,et al.  Qualitative analysis of discrete-time switched systems , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

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

[30]  Guang-Hong Yang,et al.  $H_{\infty}$ Controller Synthesis via Switched PDC Scheme for Discrete-Time T--S Fuzzy Systems , 2009, IEEE Transactions on Fuzzy Systems.