Non-fragile dissipative fuzzy control for nonlinear discrete-time systems via T-S model

The problem of the non-fragile dissipative control for the nonlinear discrete systems is dealt with. The T-S models is constructed for nonlinear systems, which makes the model approach to the original system more exact. The sufficient conditions for the existence of a dynamic output feedback fuzzy controller such that, for all admissible multiplicative controller gain variations, the closed-loop system is asymptotically stable and the dissipative performance is guaranteed, are derived in the sense of Lyapunov asymptotic stability and are formulated in the format of matrix inequalities. The sequentially linear programming matrix method (SLPMM) is applied to solve the matrix inequalities. Numerical example is provided to demonstrate the feasibility of the proposed conditions and the procedure of the controllers design.

[1]  Guang-Hong Yang,et al.  H8 control for linear systems with additive controller gain variations , 2000 .

[2]  Liu Fei,et al.  ROBUST STRICTLY DISSIPATIVE CONTROL FOR LINEAR DISCRETE TIME-DELAY SYSTEMS , 2002 .

[3]  Johan Efberg,et al.  YALMIP : A toolbox for modeling and optimization in MATLAB , 2004 .

[4]  Yang Fu-wen.  Robust and Non-fragile H_∞ Control for Discrete-time Uncertain Linear Systems , 2005 .

[5]  Lihua Xie,et al.  Dissipative control for linear discrete-time systems , 1999, Autom..

[6]  Zhang Gui-jun.  T-S model-based non-fragile guaranteed cost fuzzy control for nonlinear systems , 2006 .

[7]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[8]  P. Moylan,et al.  The stability of nonlinear dissipative systems , 1976 .

[9]  Lihua Xie,et al.  Robust dissipative control for linear systems with dissipative uncertainty and nonlinear perturbation , 1997 .

[10]  Kazuo Tanaka,et al.  Stability analysis and design of fuzzy control systems , 1992 .

[11]  Farid Sheikholeslam,et al.  Stability analysis and design of fuzzy control systems , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[12]  Friedemann Leibfritz,et al.  An LMI-Based Algorithm for Designing Suboptimal Static H2/Hinfinity Output Feedback Controllers , 2000, SIAM J. Control. Optim..

[13]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[14]  Jianliang Wang,et al.  Non-fragile Hinfinity control for linear systems with multiplicative controller gain variations , 2001, Autom..

[15]  Guan Xinping.  Resilient guaranteed cost control for a class of 2-D uncertain discrete systems , 2004 .

[16]  Lihua Xie,et al.  H/sub infinity / control and quadratic stabilization of systems with parameter uncertainty via output feedback , 1992 .