Dissipation Analysis And Control For T-S Fuzzy System With Time Delay

Fuzzy system model can express many nonlinear systems and it has the characteristics of strong robustness. The proposition of T-S fuzzy system can not only widen the research field of fuzzy control, but also can approximate many nonlinear systems by arbitrary accuracy. Moreover, dissipation is an important index in control system, and the study of it cannot be neglected. Besides, in many engineering systems, the appearance of singularity, time, actuator saturation, Markov jump is very common and even inevitable.In this paper, normal and singular T-S fuzzy models are considered, which are under the influence of time-varying delay, actuator saturation, Markov jump and so on. Based on the Lyaounov theory, linear matrix inequalities technology, reciprocally convex combination lemma and other theories, the problem of dissipation is demonstrated and the memory and non-fragile feedback controllers are designed. The main researches are as follows:Firstly, the problem of memory dissipative control for T-S fuzzy time-delay system subject to actuator saturation is considered. The Wirtinger inequality is adopted to develop new delay-dependent stability conditions, which guarantee that the closed-loop system is dissipative. And the memory controller is obtained by solving LMIs.Secondly, the problem of memory dissipative control for singular T-S fuzzy time-varying delay systems under actuator saturation is considered. A delay-central-point method and Wirtinger inequality are presented to develop less conservative delay-dependent conditions.Finally, the problem of non-fragile fuzzy dissipative control for singular Markovian jump systems with time-varying delay is investigated. Based on the mode-dependent Lyapunov function and the reciprocally convex combination lemma, sufficient conditions are obtained. And the non-fragile state feedback controller is designed.