Robust stability of impulsive Takagi–Sugeno fuzzy systems with parametric uncertainties

This paper presents a kind of time-varying impulsive Takagi–Sugeno (T–S) fuzzy model with parametric uncertainties in which each subsystem of the model is time-varying. Several robust stabilities of time-varying systems with parametric uncertainties, such as general robust stability, robustly asymptotical stability and exponential stability, are studied using uniformly positive definite matrix functions and the Lyapunov method. Specifically, robust stability conditions of time-invariant impulsive T–S fuzzy systems are also derived in the formulation of quasi-linear matrix inequalities (QLMIs) and an iterative LMIs algorithm is designed for solving QLMIs. Finally, a unified chaotic system with continuous periodic switch and a unified time-invariant chaotic system are used for demonstrating the effectiveness of our respective results.