Abstract-Till now, there are lots of stability and stabilization results about T-S (Takagi-Sugeno) fuzzy systems with time delay, but most of them are independent of the analysis of membership functions. Since the membership functions are an essential component to make a fuzzy system different from others, the conditions without its information are conservative. In this brief paper, a new Lyapunov-Krasovskii functional is designed to investigate the stability and stabilization of continuous-time T-S fuzzy systems with time delay. Different from the existing results in the literature, the integrand of the Lyapunov-Krasovskii functional in this paper depends not only on the integral variable but also on the membership functions, and thus, the information of the time-derivative of membership functions can also be used to reduce the conservativeness of finding the maximum delay bounds. Utilizing the information of the time-derivative of membership, a bunch of controllers are designed according to their sign, and then a switching idea is applied to stabilize the fuzzy system. In the end, two examples are given to illustrate the feasibility and validity of the design and analysis.

In this technical paper, a new Lyapunov-Krasovskii functional (LKF) is designed to study the stability of continuous-time Takagi-Sugeno fuzzy systems with time-varying delay. The integrand of the LKF depends on integral variable and time t which can help to reduce the number of linear matrix inequalities (LMIs). Then, a new stability criterion is derived by analyzing the sign of the time derivatives of membership functions. Compared with the existing results, larger delay bounds can be obtained by applying the new criterion. In the end, two examples show the effectiveness of the conclusions.

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