Improved results on nonlinear perturbed T-S fuzzy system with mixed delays

This paper addresses the stability criteria of nonlinear perturbed T-S fuzzy system in the appearance of distributed delay and time-varying discrete delay simultaneously. A delay partitioning method is used to separate the time-varying delay interval into multiple subintervals equivalently. Meanwhile, integral partitioning method is employed to deal with the distributed delays by dividing the distributed delay [0d] into L different segments. In order to improve the stability conditions, a new form of Lyapunov-Krasovskii functional (LKF) is presented in terms of the delay partitioning methods, which is compounded of the augmented factors related to each delay subintervals. Moreover, recently developed free-matrix-based integral inequality and extended reciprocal convex combination are applied to avoid the overabundance of the enlargement when dealing with the derivative of the LKF. Then, much less conservative stability criteria are presented. At the end, numerical examples are conducted to demonstrate the effectiveness of this proposed approach.