Robust Static Output Feedback Fuzzy Control Design for Nonlinear Discrete-Time Systems with Persistent Bounded Disturbances

tional control methods for nonlinear discrete-time systems with persistent bounded disturbances. This study introduces static output feedback fuzzy control scheme to deal with the nonlinear l ∞ -gain control problem. The structure of static output feedback fuzzy control is simpler than that of dynamic output feedback fuzzy control. Based on the Takagi and Sugeno (T-S) fuzzy model, a static output feedback fuzzy controller is developed to minimize the upper bound of l ∞ -gain of the closed-loop system under some linear matrix inequality (LMI) constraints. A singular value decomposition (SVD) method is proposed in this study to solve the l ∞ -gain static output feedback fuzzy control problem for the nonlinear discrete-time systems in terms of solving an LMI-based minimization problem. The proposed static output feedback fuzzy control scheme can efficiently attenuate the peak of perturbation due to persistent bounded disturbances for the nonlinear discrete-time systems. Simulation examples are given to illustrate the design procedures and to confirm the l ∞ -gain performance of the proposed method.

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

[2]  Sing Kiong Nguang,et al.  Static output feedback controller design for fuzzy systems: an ILMI approach , 2006, 2006 1st International Symposium on Systems and Control in Aerospace and Astronautics.

[3]  C. Peng,et al.  On Delay-dependent Robust Stability Criteria for Uncertain T-S Fuzzy Systems with Interval Time-varying Delay , 2011 .

[4]  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).

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

[6]  Wen-June Wang,et al.  T-S Fuzzy Model Based H∞ Finite-Time Synchronization Design for Chaotic Systems , 2011 .

[7]  Chung-Shi Tseng,et al.  Fuzzy observer-based fuzzy control design for nonlinear systems with persistent bounded disturbances , 2007, Fuzzy Sets Syst..

[8]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[9]  Wen-Jer Chang,et al.  Evolutionary design of static output feedback controller for Takagi-Sugeno fuzzy systems , 2007 .

[10]  P. Gahinet,et al.  H∞ design with pole placement constraints: an LMI approach , 1996, IEEE Trans. Autom. Control..

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

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

[13]  Gang Feng,et al.  H/sub /spl infin// output feedback control of discrete-time fuzzy systems with application to chaos control , 2005, IEEE Transactions on Fuzzy Systems.

[14]  Alan J. Laub,et al.  The LMI control toolbox , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[15]  Likui Wang,et al.  Robust ∞ H Fuzzy Output Feedback Control for Uncertain Discrete-time Nonlinear Systems , 2010 .

[16]  Song-Shyong Chen,et al.  Static output feedback stabilization for nonlinear interval time-delay systems via fuzzy control approach , 2004, Fuzzy Sets Syst..

[17]  Yung-Sheng Liu,et al.  A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems , 2003, SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483).

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

[19]  Thierry-Marie Guerra,et al.  Conditions of output stabilization for nonlinear models in the Takagi-Sugeno's form , 2006, Fuzzy Sets Syst..

[20]  Sheng-Luen Chung,et al.  Robust static output-feedback stabilization for nonlinear discrete-time systems with time delay via fuzzy control approach , 2005, IEEE Trans. Fuzzy Syst..

[21]  J. Pearson,et al.  l^{1} -optimal feedback controllers for MIMO discrete-time systems , 1987 .

[22]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[23]  Chung-Shi Tseng,et al.  Model reference output feedback fuzzy tracking control design for nonlinear discrete-time systems with time-delay , 2006, IEEE Transactions on Fuzzy Systems.

[24]  J. Shamma.  Nonlinear state feedback for l 1 optimal control , 1993 .