Hinfinity controller design of fuzzy dynamic systems based on piecewise Lyapunov functions.

This paper presents a controller design method for fuzzy dynamic systems based on a piecewise smooth Lyapunov function. The basic idea of the proposed approach is to construct controllers for the fuzzy dynamic systems in such a way that a piecewise continuous Lyapunov function can be used to establish the global stability with Hinfinity performance of the resulting closed loop fuzzy control systems. It is shown that the control law can be obtained by solving a set of Linear Matrix Inequalities (LMI) that is numerically feasible with commercially available software. An example is given to illustrate the application of the proposed method.

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

[2]  Jian Ma,et al.  Dynamic output feedback controller design for fuzzy systems , 2000, IEEE Trans. Syst. Man Cybern. Part B.

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

[4]  Li-Xin Wang.  Stable adaptive fuzzy control of nonlinear systems , 1993, IEEE Trans. Fuzzy Syst..

[5]  M. Tomizuka,et al.  Stability of fuzzy linguistic control systems , 1990, 29th IEEE Conference on Decision and Control.

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

[7]  R. Rovatti,et al.  On the approximation capabilities of the homogeneous Takagi-Sugeno model , 1996, Proceedings of IEEE 5th International Fuzzy Systems.

[8]  Gang Feng,et al.  Analysis and design for a class of complex control systems part II: Fuzzy controller design , 1997, Autom..

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

[10]  Wjm Walter Kickert,et al.  ANALYSIS OF A FUZZY LOGIC CONTROLLER , 1978 .

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

[12]  G. Feng.  Approaches to quadratic stabilization of uncertain fuzzy dynamic systems , 2001 .

[13]  Gang Feng,et al.  Analysis and design of fuzzy control systems using dynamic fuzzy-state space models , 1999, IEEE Trans. Fuzzy Syst..

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

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

[16]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[17]  R. M. Tong,et al.  A control engineering review of fuzzy systems , 1977, Autom..

[18]  M. Sugeno,et al.  Fuzzy Control of Model Car , 1985 .

[19]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

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

[21]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

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

[23]  Gang Feng,et al.  Analysis and design for a class of complex control systems Part I: Fuzzy modelling and identification , 1997, Autom..

[24]  Gang Feng,et al.  Analysis and design of fuzzy control systems using dynamic fuzzy global models , 1995, Fuzzy Sets Syst..

[25]  Ebrahim Mamdani,et al.  Applications of fuzzy algorithms for control of a simple dynamic plant , 1974 .

[26]  Kazuo Tanaka,et al.  A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer , 1994, IEEE Trans. Fuzzy Syst..

[27]  M. Sugeno,et al.  Structure identification of fuzzy model , 1988 .

[28]  Shu-Guang Cao,et al.  Design of fuzzy control systems with guaranteed stability , 1997, Fuzzy Sets Syst..

[29]  Michio Sugeno,et al.  Industrial Applications of Fuzzy Control , 1985 .