Stability and Stabilization of Takagi–Sugeno Fuzzy Systems With Hybrid Time-Varying Delays

Abstract

This paper investigates the stability and stabilization of Takagi–Sugeno (T–S) fuzzy systems with discrete and distributed time-varying delays. First, $p$ th moment global exponential stability ( $p\geq 1$ ) of the addressed delayed fuzzy systems is considered by virtue of the comparison approach and inequality techniques. The developed algebraic criteria include some existing outcomes as special cases. Second, global exponential stabilization of the underlying delayed fuzzy systems is performed under a fuzzy state feedback controller. Third, considering that only a few studies have been concerned with finite-time stabilization of T–S fuzzy systems, by employing the comparison strategy and a nonlinear controller, finite-time stabilization of the nominated delayed fuzzy systems is presented. The result obtained herein establishes a general theoretical framework to analyze the finite-time behavior of delayed T–S fuzzy systems. Finally, simulation examples are conducted to illustrate the validity of the results.