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

This brief paper investigates the local stabilization for continues-time Takagi-Sugeno fuzzy systems with constant time delay. In order to deal with the time delay, we design a Lyapunov-Krasovskii functional that is dependent on the membership function. Based on the Lyapunov-Krasovskii functional and the analysis of the time derivative of the membership function, less conservative results can be obtained; however, the Lyapunov-Krasovskii functional is designed so complicated that the Lyapunov level set is hard to be measured directly. Alternatively, two sets are obtained to estimate the local stabilization. One set is for the time-varying initial conditions and the other is for the time-invariant initial conditions. The relationship between the two sets are also discussed. In the end, two examples are given to illustrate the effectiveness of the proposed approach.