Static Output Feedback Control for Interval Type‐2 T‐S Fuzzy Systems Based on Fuzzy Lyapunov Functions

This study aims to design an interval type‐2 (IT2) fuzzy static output feedback controller to stabilize the IT2 Takagi‐Sugeno (T‐S) fuzzy system. Conservative results may be obtained when a common quadratic Lyapunov function is utilized to investigate the stability of T‐S fuzzy systems. A fuzzy Lyapunov function is employed in this study to analyze the stability of the IT2 fuzzy closed‐loop system formed by the IT2 T‐S fuzzy model and the IT2 fuzzy static output feedback controller. Stability conditions in the form of linear matrix inequalities are derived. Several slack matrices are introduced to further reduce the conservativeness of stability analysis. The membership‐function shape‐dependent analysis approach is also employed to relax the stability results. The numerical examples illustrate the effectiveness of the proposed conditions.

[1]  Karl-Erik Årzén,et al.  Piecewise quadratic stability of fuzzy systems , 1999, IEEE Trans. Fuzzy Syst..

[2]  Euntai Kim,et al.  New approaches to relaxed quadratic stability condition of fuzzy control systems , 2000, IEEE Trans. Fuzzy Syst..

[3]  Marcelo C. M. Teixeira,et al.  On relaxed LMI-based designs for fuzzy regulators and fuzzy observers , 2001, 2001 European Control Conference (ECC).

[4]  G. Feng,et al.  Controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[5]  J. Mendel.  Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions , 2001 .

[6]  Ji-Chang Lo,et al.  Robust H/sub /spl infin// nonlinear control via fuzzy static output feedback , 2003 .

[7]  L. Xiaodong,et al.  New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI , 2003, Autom..

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

[9]  Xiaodong Liu,et al.  New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI , 2003, Autom..

[10]  Gang Feng.  Controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions , 2003, IEEE Trans. Fuzzy Syst..

[11]  P. Shi,et al.  ROBUST H∞ STATIC OUTPUT FEEDBACK CONTROL OF FUZZY SYSTEMS: AN ILMI APPROACH , 2005 .

[12]  Hak-Keung Lam,et al.  LMI-based Stability and Performance Conditions for Continuous-time Nonlinear Systems in Takagi-Sugeno's Form , 2006, 2006 IEEE International Conference on Fuzzy Systems.

[13]  Sing Kiong Nguang,et al.  Robust H/sub /spl infin// static output feedback control of fuzzy systems: an ILMI approach , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[14]  Peng Yang,et al.  Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takagi-Sugeno's form , 2006, Autom..

[15]  Chun-Hsiung Fang,et al.  A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems , 2006, IEEE Trans. Fuzzy Syst..

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

[17]  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).

[18]  Chun-Hsiung Fang,et al.  Robust H∞ fuzzy static output feedback control of T-S fuzzy systems with parametric uncertainties , 2007, Fuzzy Sets Syst..

[19]  Antonio Sala,et al.  Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem , 2007, Fuzzy Sets Syst..

[20]  Kazuo Tanaka,et al.  A Descriptor System Approach to Fuzzy Control System Design via Fuzzy Lyapunov Functions , 2007, IEEE Transactions on Fuzzy Systems.

[21]  Hak-Keung Lam,et al.  Stability Analysis of Interval Type-2 Fuzzy-Model-Based Control Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[22]  Huai-Ning Wu,et al.  An ILMI approach to robust I static output feedback fuzzy control for uncertain discrete-time nonlinear systems , 2008, Autom..

[23]  Baocang Ding,et al.  Poly‐quadratic stability of discrete‐time nonlinear systems in Takagi‐Sugeno's form , 2009 .

[24]  Guang-Hong Yang,et al.  H∞ fuzzy static output feedback control of T‐S fuzzy systems based on fuzzy Lyapunov approach , 2009 .

[25]  Reinaldo M. Palhares,et al.  A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems , 2009, Inf. Sci..

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

[27]  Ho Jae Lee,et al.  Fuzzy Static Output Feedback May Be Possible in LMI Framework , 2009, IEEE Transactions on Fuzzy Systems.

[28]  Guanghong Yang,et al.  Static output feedback H ∞ control of a class of nonlinear discrete-time systems , 2009 .

[29]  Mohammed Chadli,et al.  An LMI approach to design observer for unknown inputs Takagi‐Sugeno fuzzy models , 2010 .

[30]  Jerry M. Mendel,et al.  On the Stability of Interval Type-2 TSK Fuzzy Logic Control Systems , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[31]  M. Sami Fadali,et al.  Stability Analysis and Control of Discrete Type-1 and Type-2 TSK Fuzzy Systems: Part II. Control Design , 2011, IEEE Transactions on Fuzzy Systems.

[32]  M. Sami Fadali,et al.  Stability Analysis and Control of Discrete Type-1 and Type-2 TSK Fuzzy Systems: Part I. Stability Analysis , 2011, IEEE Transactions on Fuzzy Systems.

[33]  Jin Bae Park,et al.  A New Fuzzy Lyapunov Function for Relaxed Stability Condition of Continuous-Time Takagi–Sugeno Fuzzy Systems , 2011, IEEE Transactions on Fuzzy Systems.

[34]  Xiangpeng Xie,et al.  Relaxed Stability Conditions for Continuous-Time T–S Fuzzy-Control Systems Via Augmented Multi-Indexed Matrix Approach , 2011, IEEE Transactions on Fuzzy Systems.

[35]  Wei Chang,et al.  Robust fuzzy control for continuous perturbed time-delay affine takagi–sugeno fuzzy models† , 2011 .

[36]  Salim Labiod,et al.  Robust H∞ static output feedback stabilization of T-S fuzzy systems subject to actuator saturation , 2012 .

[37]  A. Jiménez,et al.  Improvement of Takagi‐Sugeno fuzzy model for the estimation of nonlinear functions , 2012 .

[38]  Jianbin Qiu,et al.  Observer-Based Piecewise Affine Output Feedback Controller Synthesis of Continuous-Time T–S Fuzzy Affine Dynamic Systems Using Quantized Measurements , 2012, IEEE Transactions on Fuzzy Systems.

[39]  Chinyao Low,et al.  Single machine group scheduling with learning effects and past-sequence-dependent setup times , 2012, Int. J. Syst. Sci..