Stabilization of discrete-time T-S fuzzy systems with random input delay: A new modeling method

This paper is concerned with the problems of stability analysis and stabilization control design for a class of discrete-time T-S fuzzy systems with random input delay. Different from the common assumptions on the delay in the existing literatures, it is assumed in this paper that the probabilities of the delay taking each value in a finite point set are known. In terms of the information of the occurrence probabilities of the delay taking values in the two finite point sets, using state augmentation method, a new state space model of the discrete-time T-S fuzzy systems are derived. Based on the new model, some criteria for the stochastic stability analysis and stabilization controller design are derived by using the Lyapunov-Krasovskii functional method. The developed criteria are in the form of linear matrix inequalities(LMIs). Finally, an illustrative example is provided to show the effectiveness and applicability of the proposed method.