Fuzzy-Model-Based ${{\cal D}}$-Stability and Nonfragile Control for Discrete-Time Descriptor Systems With Multiple Delays

Abstract

This paper is concerned with the problems of D-stability and nonfragile control for a class of discrete-time descriptor Takagi-Sugeno (T-S) fuzzy systems with multiple state delays. D-stability criteria are proposed to ensure that all the poles of the descriptor T-S fuzzy system are located within a disk contained in the unit circle. Furthermore, a sufficient condition is presented such that the closed-loop system is regular, causal, and D-stable, in spite of parameter uncertainties and multiple state delays. The corresponding solvability conditions for the desired fuzzy-rule-dependent nonfragile controllers are also established. Finally, examples are given to show the effectiveness and advantages of the proposed techniques.