Fuzzy Output Feedback Control Design for Nonlinear Systems: An LMI Approach

This paper addresses the problem of stabilizing a class of nonlinear systems by using an fuzzy output feedback controller. First, a class of nonlinear systems is approximated by a Takagi-Sugeno (TS) fuzzy model. Then, based on a well-known Lyapunov functional approach, we develop a technique for designing an fuzzy output feedback control law which guarantees the gain from an exogenous input to a regulated output is less or equal to a prescribed value. A design algorithm for constructing an fuzzy output feedback controller is given. In contrast to the existing results, the premise variables of the fuzzy output feedback controller are not necessarily to be the same as the premise variables of the TS fuzzy model of the plant. A numerical simulation example is presented to illustrate the theory development.

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

[2]  P. Moylan,et al.  Dissipative Dynamical Systems: Basic Input-Output and State Properties , 1980 .

[3]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

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

[5]  J. Helton,et al.  H" CONTROL FOR NONLINEAR PLANTS: CONNECTIONS WITH DIFFERENTIAL GAMES , 1989 .

[6]  A. Schaft.  On a state space approach to nonlinear H ∞ control , 1991 .

[7]  Tamer Bąar.  Optimum performance levels for minimax filters, predictors and smoothers , 1991 .

[8]  A. Isidori,et al.  Disturbance attenuation and H/sub infinity /-control via measurement feedback in nonlinear systems , 1992 .

[9]  A. Isidori.  Feedback control of nonlinear systems , 1992 .

[10]  A. Schaft.  L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback H/sub infinity / control , 1992 .

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

[12]  Chieh-Li Chen,et al.  Analysis and design of fuzzy control system , 1993 .

[13]  J. Helton,et al.  H∞ control for nonlinear systems with output feedback , 1993, IEEE Trans. Autom. Control..

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

[15]  Kazuo Tanaka,et al.  Stability and stabilizability of fuzzy-neural-linear control systems , 1995, IEEE Trans. Fuzzy Syst..

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

[17]  Minyue Fu,et al.  Robust nonlinear H∞ filtering , 1996, Autom..

[18]  Li-Xin Wang,et al.  A Course In Fuzzy Systems and Control , 1996 .

[19]  Kazuo Tanaka,et al.  Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H∞ control theory, and linear matrix inequalities , 1996, IEEE Trans. Fuzzy Syst..

[20]  Gang Feng,et al.  Quadratic stability analysis and design of continuous-time fuzzy control systems , 1996, Int. J. Syst. Sci..

[21]  Zengqi Sun,et al.  Analysis and design of fuzzy controller and fuzzy observer , 1998, IEEE Trans. Fuzzy Syst..

[22]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[23]  Marcelo C. M. Teixeira,et al.  Stabilizing controller design for uncertain nonlinear systems using fuzzy models , 1999, IEEE Trans. Fuzzy Syst..

[24]  Stanislaw H. Zak,et al.  Stabilizing fuzzy system models using linear controllers , 1999, IEEE Trans. Fuzzy Syst..

[25]  Bor-Sen Chen,et al.  Mixed H2/H∞ fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach , 2000, IEEE Trans. Fuzzy Syst..

[26]  Bor-Sen Chen,et al.  Mixed Fuzzy Output Feedback Control Design for Nonlinear Dynamic Systems: An LMI Approach , 2000 .

[27]  P. Shi,et al.  Stabilisation of a class of nonlinear time-delay systems using fuzzy models , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).