T-S fuzzy modeling and control for a class of chaotic (hyperchaotic) systems with uncertain parameters

A novel T-S fuzzy model-based method is proposed for controlling a class of chaotic (hyperchaotic) systems with uncertain parameters. The interval matrix theory is applied to describe the parametric uncertainty. The T-S fuzzy model is employed for accurately modeling the chaotic (hyperchaotic) systems. Based on the T-S fuzzy model, the parallel distributed compensation (PDC) technique is applied to design a state feedback controller for the chaotic (hyperchaotic) systems. By using Lyapunov stability theory, the robust stability of the closed-loop system is proved. The new scheme considers the interactions of the fuzzy sub-systems sufficiently. The gain matrices of the controller can be obtained by solving a set of linear matrix inequalities (LMIs). Simulation results are presented to demonstrate the effectiveness of the proposed method.