In this paper, we present an output feedback controller using a fuzzy controller and observer for nonlinear systems with unknown time-delay. Recently, Cao et al. proposed a stabilization method for the nonlinear time-delay systems using a fuzzy controller when the time-delay is known. In general, however, it is impossible to know or measure this time-varying delay. The proposed method requires only the upper bound of the derivative of the time-delay. We represent the nonlinear system with the unknown time-delay by Takagi-Sugeno (T-S) fuzzy model and design the fuzzy controller and observer for the systems using the parallel distributed compensation (PDC) scheme. In addition, we derive the sufficient condition for the asymptotic stability of the equilibrium point by applying Lyapunov-Krasovskii theorem to the closed-loop system and solve the condition in the formulation of LMI. Finally, computer simulations are included to demonstrate the effectiveness of the suggested method.

This paper presents a fuzzy model-based approach for synchronization of time-delay chaotic system with input saturation. Time-delay chaotic drive and response system is respectively represented by Takagi-Sugeno (T-S) fuzzy model. Specially, the response system contains input saturation. Using the unidirectional linear error feedback and the parallel distributed compensation (PDC) scheme, we design fuzzy chaotic synchronization system and analyze local stability for synchronization error dynamics. Since time-delay in the transmission channel always exists, we also take it into consideration. The sufficient condition for the local stability of the fuzzy synchronization system with input saturation and channel time-delay is derived by applying Lyapunov-Krasovskii theory and solving linear matrix inequalities (LMI's) problem. Numerical examples are given to demonstrate the validity of the proposed approach.