Membership function dependent stability criterion for T-S fuzzy systems with time delay via a non-uniform delay partitioning approach

The problem of stability for T-S fuzzy systems with time delay is concerned in this paper. Firstly, in order to make full use of the information of time delay, a non-uniform delay partitioning approach is proposed by introducing a known adjusting parameter. Secondly, the fuzzy line-integral function and an appropriate Lyapunov-Krasovskii(L-K) functional are constructed based on Lyapunov stability theory. Then, the integral terms from the derivation of L-K functional are estimated by Wirtinger integral inequality, which can effectively reduce the conservatism of results compared with Jensen integral inequality. Thirdly, a less conservative membership function dependent stability criterion is established. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.