On improvement of stability conditions for continuous Mamdani-like fuzzy systems

This paper is concerned with continuous fuzzy systems with singleton consequents, called type II fuzzy systems. It first introduces the canonical form of an unforced type II fuzzy system and its stability theorem presented in the previous study. Then, improving the stability theorem, it gives necessary and sufficient conditions such that a type II fuzzy system is stable with respect to a global quadratic Lyapunov function.

[1]  M. Braae,et al.  Theoretical and linguistic aspects of the fuzzy logic controller , 1979, Autom..

[2]  T. Takagi,et al.  A New Approach to Design of Fuzzy Controller , 1983 .

[3]  D. Dutta Majumder,et al.  Application of circle criteria for stability analysis of linear SISO and MIMO systems associated with fuzzy logic controller , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[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]  Javier Aracil,et al.  Stability Analysis of Fuzzy Control Systems Based on the Conicity Criterion. , 1993 .

[6]  E. H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Man Mach. Stud..

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

[8]  Takeshi Furuhashi,et al.  On Design of Fuzzy Controllers Using Fuzzy Models and Modifications of Control Rules Based on Descriptions of Dynamical Behavior of Control Systems , 1995 .

[9]  Ryozo Katoh,et al.  Stability analysis of control system having PD type of fuzzy controller , 1995, Fuzzy Sets Syst..

[10]  Sylvie Galichet,et al.  Fuzzy controllers: synthesis and equivalences , 1995, IEEE Trans. Fuzzy Syst..

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

[12]  László T. Kóczy,et al.  Fuzzy if... then rule models and their transformation into one another , 1996, IEEE Trans. Syst. Man Cybern. Part A.

[13]  Kazuo Tanaka,et al.  An LMI approach to fuzzy controller designs based on relaxed stability conditions , 1997, Proceedings of 6th International Fuzzy Systems Conference.

[14]  Fengming Song,et al.  Constructive theory for fuzzy systems , 1997, Fuzzy Sets Syst..

[15]  T. Vincent,et al.  Nonlinear and Optimal Control Systems , 1997 .

[16]  Michio Sugeno,et al.  Stabilizing Control of Fuzzy Systems with Singleton Consequents , 1998 .

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

[18]  M. Sugeno,et al.  A construction procedure of a Lyapunov function in stability analysis of fuzzy systems with singleton consequents , 1999, IEEE SMC'99 Conference Proceedings. 1999 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.99CH37028).

[19]  M. Sugeno,et al.  Stability conditions for closed-loop fuzzy systems with singleton consequents , 1999, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

[20]  Michio Sugeno,et al.  On stability of fuzzy systems expressed by fuzzy rules with singleton consequents , 1999, IEEE Trans. Fuzzy Syst..