Filtering Design And Stabilization Analysis With Time Delay In Systems For Continuous-time Takagi-Sugeno Fuzzy Model

The non-quadratic Lyapunov function contains more variables and hence is less conservative than the classical quadratic Lyapunov function.Based on the existing results,the H_? fuzzy filtering design and stabilization analysis with time-varying delay for T-S fuzzy system have been studied in this paper by applying the non-quadratic Lyapunov function.The main contents are as follows:The H_? fuzzy filtering design for continuous-time T-S fuzzy system is studied.First,the time derivatives of the membership functions are analyzed and the results are transformed into LMIs(Linear Matrix Inequalities)by applying the convex tool.Then,a new non-quadratic Lyapunov function,which has the diagonal form,is designed to get some LMIs to design the filtering.In the end,a numerical example is given to show the effectiveness of the proposed approach.Stabilization analysis for continuous time T-S fuzzy model with time-varying delay.First,the non-parallel distributed compensation law is designed and the bound of the time derivative of the membership function is discussed.Some LMIs are obtained by applying the convex tool and Schur complement to ensure the bound of the time derivative of the membership functions.Then,delay independent stabilization result is obtained by using the Ltapunov-Razumikhin theory.Next,delay dependent stabilization results are obtained by designing a Lyapunov-Krasovskii functional.Furthermore,a new controller which contains time delay is designed and some slack variables are introduced,in addition,membership function dependent Lyapunov-Krasovskii functional is constructed.All of these help us to get some less conservative stabilization results.In the end,the simulation demonstrate the effectiveness of the method in this paper.