Stability Analysis And Stabilization Control Of TS Fuzzy Systems With Time-varying Delays

In the past thirty years, Takagi-Sugeno fuzzy system has been widely applied in practice. In this thesis, the stability analysis and stabilization problem for T-S fuzzy systems with time-varying delay are studied. By constructing an augmented Lyapunov-Krasovskii functional and using the Wirtinger-based integral inequality and the reciprocally convex method, delay-dependent stability criteria and stabilization conditions are obtained in terms of strict linear matrix inequalities(LMIs). The main contents of this thesis are as follows:For T-S fuzzy systems with time-varying delay, by constructing an augmented Lyapunov-Krasovskii functional, using the Wirtinger-based integral inequality and the reciprocally convex method to deal with integral functional, we obtain sufficient conditions in terms of LMIs for the stability analysis.For T-S fuzzy control system with time-varying delay, a state feedback controller based on the stability condition is designed by constructing an augmented Lyapunov-Krasovskii functional and using appropriate variable replacement. The stabilization condition is in terms of strict LMIs.Finally, we summarize the stability analysis and stabilization of T-S fuzzy system and propose some future research work based on the present study.