Sampled-Data Fuzzy Control of Chaotic Systems Based on a T–S Fuzzy Model

Abstract

In this paper, a sampled-data fuzzy controller is designed to stabilize a class of chaotic systems. A Takagi-Sugeno (T-S) fuzzy model is employed to represent the chaotic systems. Based on this general model, the exponential stability issue of the closed-loop systems with an input constraint is first investigated by a novel time-dependent Lyapunov functional, which is positive definite at sampling times but not necessary between the sampling times. Then, two sufficient conditions are developed for sampled-data fuzzy controller synthesis of the underlying T-S fuzzy model with or without input constraint. All the proposed results in this paper depend on both the upper and lower bounds on a sampling interval, and the available information about the actual sampling pattern is fully utilized. The proposed sampled-data fuzzy control scheme is successfully applied to the chaotic Lorenz system, which is shown to be effective and less conservative compared with existing results.