Improved results on perturbed T-S fuzzy systems with mixed delays using geometric sequence division related partitioning methods.

This paper addresses improved stability results for T-S fuzzy systems with mixed delays and nonlinear perturbations. By introducing the geometric sequence division (GSD) method, the discrete delay interval can be separated into multiple subintervals with unequal lengths based on the common ratio α. Meanwhile integral partitioning method is applied to deal with the distributed delay. A Lyapunov-Krasovskii functional (LKF) is newly established with augmented factors and triple integral terms which are constructed by means of the length of every subintervals. In addition, in order to reduce the enlargement when we deal with the estimation of the LKF derivative, a free-matrix-based integral inequality, an extended reciprocal convex combination, and free weight matrices techniques are employed. A stability analysis of the delayed T-S fuzzy systems is presented with much less conservative criteria. At the end numerical examples are given to demonstrate the significant improvements of this proposed design. [ABSTRACT FROM AUTHOR]