Robust fuzzy control for chaotic (hyperchaotic) systems with parametric uncertainties based on LMI technique

A novel robust fuzzy controller design method is proposed to stabilize a class of chaotic (hyperchaotic) systems with uncertain parameters based on their equivalent T-S fuzzy models. In this method, the interval system theory is applied to deal with the parametric uncertainty firstly, and then a fuzzy state feedback controller is designed to stabilize the equilibrium of the uncertain chaotic (hyperchaotic) systems robustly based on exact linearization (EL) theory and parallel distributed compensation (PDC) technique. Moreover, the sufficient criterion for the robust stability of the equilibrium of the controlled uncertain chaotic (hyperchaotic) systems is derived by Lyapunov stability theory and LMI technique. The designed controller with simple structure and rapid response can stabilize many kinds of uncertain chaotic or hyperchaotic systems. Simulation results are presented to demonstrate the effectiveness of the proposed method.