Local Stability and Local Stabilization of Discrete-time T-S Fuzzy Systems with Time-delay

The goal of this paper is to propose linear matrix inequality (LMI) formulations to analyze the local stability and local stabilization of discrete-time nonlinear systems represented by Takagi-Sugeno (T-S) fuzzy systems with time-delay. In order to estimate the domain of attraction (DA) of the time-delay systems, the so-called fuzzy Lyapunov-Krasovskii functionals are used to characterize the subsets of the DA as sublevel sets of the Lyapunov-Krasovskii functionals. We use the information of the variation rates of the membership functions to obtain less conservative results. Finally, examples are given to illustrate the proposed methods.