H∞ control design for discrete-time switched fuzzy systems

Abstract This paper investigates the H ∞ control design and asynchronous stabilization problems for a class of discrete-time switched Takagi and Sugeno (T–S) fuzzy systems. The studied fuzzy systems have two level functions, namely, crisp switching functions and local fuzzy weighting functions, which inherently contain the features of switched hybrid systems and T–S fuzzy systems. In addition, the considered switching instants have asynchronous phenomena between the system switching modes and the controller switching modes. Based on the theory of the switching Lyapunov stability and average-dwell time method, both the matched H ∞ state feedback controllers and the unmatched state feedback controllers are designed. Moreover, the global uniformly asymptotically stability (GUAS) conditions are proposed and 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]  Honghai Liu,et al.  Reliable Fuzzy Control for Active Suspension Systems With Actuator Delay and Fault , 2012, IEEE Transactions on Fuzzy Systems.

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

[3]  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).

[4]  Guang-Hong Yang,et al.  Dynamic Output Feedback Control Synthesis for Continuous-Time T–S Fuzzy Systems via a Switched Fuzzy Control Scheme , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  Xiaoping Liu,et al.  Robust Hinfinity control of Takagi-Sugeno fuzzy systems with state and input time delays , 2009, Fuzzy Sets Syst..

[6]  Honghai Liu,et al.  Adaptive Sliding-Mode Control for Nonlinear Active Suspension Vehicle Systems Using T–S Fuzzy Approach , 2013, IEEE Transactions on Industrial Electronics.

[7]  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).

[8]  J. Chiou,et al.  Analysis and synthesis of switched nonlinear systems using the T–S fuzzy model , 2010 .

[9]  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.

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

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

[13]  L. Zadeh,et al.  An editorial perspective , 1978 .

[14]  Hak-Keung Lam,et al.  Polynomial Fuzzy-Model-Based Control Systems: Stability Analysis Via Piecewise-Linear Membership Functions , 2011, IEEE Transactions on Fuzzy Systems.

[15]  Huai-Ning Wu,et al.  Reliable LQ fuzzy control for nonlinear discrete-time systems via LMIs , 2004, IEEE Trans. Syst. Man Cybern. Part B.

[16]  Guang-Hong Yang,et al.  Robust H∞∞ dynamic output feedback control for linear time-varying uncertain systems via switching-type controllers , 2010 .

[17]  Kazuo Tanaka,et al.  An approach to fuzzy control of nonlinear systems: stability and design issues , 1996, IEEE Trans. Fuzzy Syst..

[18]  Guang-Hong Yang,et al.  Dynamic output feedback H∞ control synthesis for discrete-time T-S fuzzy systems via switching fuzzy controllers , 2009, Fuzzy Sets Syst..

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

[20]  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).

[21]  Xiaodong Liu,et al.  Approaches to quadratic stability conditions and H∞ control designs for T-S fuzzy systems , 2003, IEEE Trans. Fuzzy Syst..

[22]  Lakmal Seneviratne,et al.  Stability analysis of polynomial fuzzy-model-based control systems under perfect/imperfect premise matching , 2011 .

[23]  Farid Sheikholeslam,et al.  L 2 -gain analysis for switched systems with a state-dependent switching signal , 2011 .

[24]  TanakaK.,et al.  Fuzzy regulators and fuzzy observers , 1998 .

[25]  Kazuo Tanaka,et al.  Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs , 1998, IEEE Trans. Fuzzy Syst..

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

[27]  H. Lam.  Polynomial Fuzzy Model-Based Control Systems: Stability Analysis and Control Synthesis Using Membership Function Dependent Techniques , 2016 .

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

[29]  Xiaodong Liu,et al.  New approaches on Hinfinity control of T-S fuzzy systems with interval time-varying delay , 2009, Fuzzy Sets Syst..

[30]  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.

[31]  Youyi Wang,et al.  H∞ and mixed H2/H∞ control of discrete-time T-S fuzzy systems with local nonlinear models , 2011, Fuzzy Sets Syst..

[32]  TanakaK.,et al.  An approach to fuzzy control of nonlinear systems , 1996 .

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

[34]  Guang-Hong Yang,et al.  Quantised feedback stabilisation of planar systems via switching-based sliding-mode control , 2012 .

[35]  Peng Shi,et al.  Stability, ${l}_{2}$ -Gain and Asynchronous ${H}_{{\infty}}$ Control of Discrete-Time Switched Systems With Average Dwell Time , 2009, IEEE Transactions on Automatic Control.

[36]  Youmin Zhang,et al.  Tolerance of intermittent faults in spacecraft attitude control: switched system approach , 2012 .

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

[38]  M. Staroswiecki,et al.  Observer-based fault-tolerant control for a class of switched nonlinear systems , 2007 .

[39]  Jun Zhao,et al.  Brief Paper - Output tracking control for a class of switched non-linear systems with partial state constraints , 2013 .

[40]  Kevin Guelton,et al.  Non-quadratic local stabilization for continuous-time Takagi-Sugeno models , 2012, Fuzzy Sets Syst..

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