A generalized probability-interval-decomposition approach for stability analysis of T-S fuzzy systems with stochastic delays

Based on the generalized probability-interval-decomposition approach, the delay-dependent stability analysis for a class of T-S fuzzy systems with stochastic delays is investigated. The information of the probability distribution of stochastic delay is fully exploited and a series of sufficient stability criteria are obtained. A rigorous mathematical proof is provided that the conservatism of the proposed stability criteria can be reduced progressively by increasing the number of the probability interval. Based on this, a novel hierarchy of LMI conditions is established. It is rigorously proved that with the same decomposition of probability interval, the conservatism of the proposed stability criteria is less than the one obtained by time-varying delay decomposition approach. The computation burden of the proposed method is analyzed and compared with one of the time-varying delay decomposition approach. Finally, a numerical example is given to illustrate the validness and effectiveness of the proposed approach.