The State Feedback Control Based on Fuzzy Observer for T-S Fuzzy Systems with Unknown Time-Delay

Hyunseok SHIN  Euntai KIM  Mignon PARK  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E86-A   No.9   pp.2333-2339
Publication Date: 2003/09/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Systems and Control
T-S fuzzy system,  time-delay,  observer-based control,  LMI,  

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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.