A flexible membership-dependent functional method to stability and stabilization for T-S fuzzy systems with interval time-varying delay

Abstract

In this paper, the stability and stabilization problems for T-S fuzzy delayed systems is studied. A flexible membership-dependent Lyapunov functional (FMDLF) is constructed to fully utilize the information of time-varying delay and fuzzy membership functions (FMFs). Different from some exiting ones, the upper and lower limits of the integral terms in the FMDLF are adjustable. By first introducing exponential gains in reciprocally convex inequality, an exponential-type reciprocally convex inequality (ETRCI) is developed to estimate the FMDLF, which generates some existing results. Based on the FMDLF and ETRCI, a novel stability criterion is obtained. By using a decoupling technique, the corresponding controller design problem is solved. Importantly, the dimensions of the solution space increase since the constraints on slack matrices in some previous studies are eliminated. The effectiveness of the proposed results can be demonstrated by some examples.