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Original Articles

Robust H fuzzy control of nonlinear systems with multiple time delays

Pages 351-360 | Received 22 Jan 2004, Accepted 12 Dec 2006, Published online: 14 Jun 2007
 

Abstract

A robustness design of fuzzy control via model-based approach is proposed in this article to overcome the effect of approximation error between multiple time-delay nonlinear systems and Takagi--Sugeno (T-S) fuzzy models. A stability criterion is derived based on Lyapunov's direct method to ensure the stability of nonlinear multiple time-delay systems especially for the resonant and chaotic systems. Positive definite matrices P and Rk of the criterion are obtained by using linear matrix inequality (LMI) optimization algorithms to solve the robust fuzzy control problem. In terms of the control scheme and this criterion, a fuzzy controller is then designed via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay system and the H control performance is achieved at the same time. Finally, two numerical examples of the chaotic and resonant systems are demonstrated to show the concepts of the proposed approach.

Acknowledgements

The authors wish to express sincere gratitude to Professor Peter Fleming for his help and the anonymous reviewers for their constructive comments and helpful suggestions, which lead to substantial improvements of this article.

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