Delay-Dependent Stability Analysis and Controller Synthesis for Discrete-Time T–S Fuzzy Systems With Time Delays

Based on a novel delay-dependent piecewise Lyapunov–Krasovskii functional (DPLKF), this paper presents delay-dependent stability analysis and synthesis methods for discrete-time Takagi–Sugeno (T–S) fuzzy systems with time delays. It is shown that the stability and stabilization with some required performance can be established for the closed loop control system if there exists a DPLKF and that the DPLKF and the corresponding controller can be obtained by solving a set of linear matrix inequalities (LMIs). New algorithms have also been developed to obtain the maximum value of the allowable constant delay and the suboptimal performance upper bound. An example is finally presented to demonstrate the efficiency and advantage of the proposed methods.