Stability criteria for T-S fuzzy systems with interval time-varying delays and nonlinear perturbations based on geometric progression delay partitioning method

摘要

In this paper, a novel delay partitioning method is proposed by introducing the theory of geometric progression for the stability analysis of T-S fuzzy systems with interval time-varying delays and non-linear perturbations. Based on the common ratio a, the delay interval is unequally separated into multiple subintervals. A newly modified Lyapunov-Krasovskii functional (LKF) is established which includes triple-integral terms and augmented factors with respect to the length of every related proportional subintervals. In addition, a recently developed free-matrix-based integral inequality is employed to avoid the overabundance of the enlargement when dealing with the derivative of the LKF. This innovative development can dramatically enhance the efficiency of obtaining the maximum upper bound of the time delay. Finally, much less conservative stability criteria are presented. Numerical examples are conducted to demonstrate the significant improvements of this proposed approach. (C) 2016 ISA. Published by Elsevier Ltd. All rights reserved.