T-s Fuzzy Systems Delay Correlation Method

With the development of technology, the practical industry processes are becoming more and more complex. These processes have characteristics, such as high nonlinearity, time-delay, many variables and uncertainty. These make it difficult to control such systems effectively by using the classical theory and the existing control methods. Based on above observation, this thesis focuses on nonlinear systems with time-varying delay. Based on T-S fuzzy model, which is extensively applied in nonlinear systems, and Lyapunov stability theories, the problems of stability analysis and stabilization via state feedback are addressed for this kind of systems by using fuzzy weighting-dependent Lyapunov-Krasovskii function, LMI approach, and free-weighting matrix technique. The research and the results in this thesis are dependent on delay-dependent method which is less conservative than delay-independent one. The main content contains two parts as follows:At first, the system with state time-delay is first considered. By means of appropriate fuzzy weighting-dependent Lyapunov-Krasovskii functions and free-weighting matrix technique, the problem of stability analysis has been discussed for this kind of systems, furthermore a sufficient condition of delay-dependent stability is proposed.Then, noting that the input-delay frequently occurs in practical systems. The problem of stabilization of systems with both state and input time-delays are addressed. A new delay-dependent control design method via state feedback has been proposed in terms of LMIs.The fuzzy weighting-dependent Lyapunov-Krasovskii function proposed in this thesis is quite different from the existing ones due to adding more fuzzy weighting to the function. In addition, the information of input time-delay is fully employed in order to obtain the less conservative results.Numerical examples are given to illustrate the effectiveness of the approaches proposed in this thesis.