Local Stabilization for Continuous-time Takagi–Sugeno Fuzzy Systems With Time Delay

Abstract

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A New Approach to Stability and Stabilization Analysis for Continuous-Time Takagi–Sugeno Fuzzy Systems With Time Delay

“…In this paper, the integrand of V 2 (x t ) and V 3 (x t ) depends not only on the integral variable s but also on the membership functions, while in [18], V 2 (x t ) and V 3 (x t ) are independent of the membership function. 2), The method to deal with the time derivatives of the membership function is completely different.…”

“…The differences between this paper and [18] are as follows: 1), The chosen Lyapunov-Krasovskii functional is different. In this paper, the integrand of V 2 (x t ) and V 3 (x t ) depends not only on the integral variable s but also on the membership functions, while in [18], V 2 (x t ) and V 3 (x t ) are independent of the membership function.…”

“…Remark 1: Note, the Lyapunov-Krasovskii functional used in Theorem 1 is different from the one used in the literature such as [11], [17], [18]. In V 2 (x t ) and V 3 (x t ) of this paper, Q h and Z h are independent of the integral variable s but on the time t, so the information of the timederivative of the membership function can be used to obtain new less conservative stability conditions, at the same time, there comes a problem that how to deal with the integral…”

“…pendent on the integral variable s, but it has been shown in [18] that this choice could not help reduce the conservativeness.…”

“…However, all of the results mentioned above are independent of the analysis of membership functions which will lead to conservativeness because the membership functions are an essential component to make a fuzzy system different from other systems. More recently, a membership function dependent Lyapunov-Krasovskii functional is designed in [18] and some less conservative results are obtained by analyzing the time derivative of the membership function, however the drawback is that the local stabilization region becomes smaller as the delay increases.…”