Research On The Stability For The T-S Fuzzy Systems With Time Delay

The analysis and design of the stability of fuzzy control systems is the important research subject in fuzzy theory. The stability is based on the control method for fuzzy systems and ensuring the performance of control systems. However, a fuzzy system is nonlinear essentially, and the analysis of the stability is more difficult. Now, although there exists some theories ensuring the stability of fuzzy systems, there is not complete theoretical system. In particular, we study further for fuzzy dynamical systems with time-delay.This paper has done the following major work:1. Firstly, we summarized systematically the development of fuzzy control system and LMI, summed up the relevant research results of the stability on fuzzy control, then make a detailed comment on the way of thinking that these results used and the impact they brought.2. Expounded two types basic model on fuzzy control system, then on the basis of the theory of Lyapunov stability, for T-S fuzzy model we summarized the stability sufficient condition when continuous fuzzy model is at the open-loop and closed-loop.3. Studied stability of a class of time-delay T-S fuzzy control system. On the basis of the theory of Lyapunov stability, for a class of time-delay T-S fuzzy model, we summarized the stability sufficient condition when a class of time-delay continuous fuzzy model is at the open-loop and closed-loop based on LMI, and proved the stability condition.4. Studied the quadratic stability of a class of time-delay continuous T-S fuzzy model, and gave sufficient conditions of quadratic stability, then proved the stability conditions based on Lyapunov theory.