Quadratic stabilization of uncertain discrete-time fuzzy dynamic systems

New approaches to quadratic stabilization of uncertain discrete-time fuzzy dynamic systems are developed in this paper. This uncertain fuzzy dynamic model is used to represent a class of uncertain discrete-time complex nonlinear systems which include both linguistic information and system uncertainties. It is shown that the uncertain fuzzy dynamic system is stabilizable if a suitable Riccati equation or a set of Riccati equations have solutions. Constructive algorithms are also developed to obtain the stabilization feedback control laws. Finally, an example is given to illustrate the application of the proposed method.

[1]  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..

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

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

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

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

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

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

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

[10]  Denis Arzelier,et al.  Robust stabilization of discrete-time linear systems with norm-bounded time-varying uncertainty , 1994 .

[11]  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..

[12]  Gang Feng,et al.  Design of Fuzzy Control Systems Based on State Feedback , 1995, J. Intell. Fuzzy Syst..

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

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

[15]  Gang Feng,et al.  An approach to H∞ control of a class of nonlinear systems , 1996, Autom..

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

[17]  Gang Feng,et al.  Analysis and design of uncertain fuzzy control systems. Part I. Fuzzy modelling and identification , 1996, Proceedings of IEEE 5th International Fuzzy Systems.

[18]  Gang Feng,et al.  Further results about quadratic stability of continuous-time fuzzy control systems , 1997, Int. J. Syst. Sci..

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

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

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

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

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

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