Abstract-This paper presents the fuzzy-model-based control approach to synchronize two chaotic systems subject to parameter uncertainties. A fuzzy state-feedback controller using the system state of response chaotic system and the time-delayed system state of drive chaotic system is employed to realize the synchronization. The time delay which complicates the system dynamics makes the analysis difficult. To investigate the system stability and facilitate the design of fuzzy controller, T-S fuzzy models are employed to represent the system dynamics of the chaotic systems. Furthermore, the membership grades of the T-S fuzzy models become uncertain due to the existence of parameter uncertainties which further complicates the system analysis. To ease the stability analysis and produce less conservative analysis result, the membership functions of both T-S fuzzy models and fuzzy controller are considered. Stability conditions are derived using Lyapunov-based approach to aid the design of fuzzy state-feedback controller to synchronize the chaotic systems. Simulation examples are presented to illustrate the merits of the proposed approach.

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For a class of T-S fuzzy time-delay systems, the problem of designing a static output feedback controller is considered via the parallel distributed compensation (PDC) approach. Namely, when one controller can not assure the stability of system, a controller switching strategy in certain set of controllers may stabilize the system. Moreover the adoption of this strategy often improves the performance of system even in the case that a single controller can stabilize the system. By defining multiple Lyapunov functions, the sufficient condition for the existence of the static out put feedback controller is presented in terms of linear matrix inequality (LMI), which guarantees the stability of the close-loop system for the switching cases. The simulation results demonstrate the effectiveness of the proposed method.

This paper investigates the problems of stability analysis and stabilization for a class of switched fuzzy discrete-time systems. Based on a common Lyapunov functional, a switching control method has been developed for the stability analysis of switched discrete-time fuzzy systems. A new stabilization approach based on a switching parallel distributed compensation scheme is given for the closed-loop switched fuzzy systems. Finally, the illustrative example is provided to demonstrate the effectiveness of the techniques proposed in this paper.