An LMI-based robust controller design using global nonlinear sliding surfaces and application to chaotic systems

This paper addresses a novel global nonlinear sliding surface to achieve robustness and high performance for a class of uncertain nonlinear systems. Using the Lyapunov stability theorem, exponential stability analysis of the system states is proposed in the linear matrix inequality form. A new control law is designed to guarantee the elimination of the reaching phase and the existence of the sliding mode around the nonlinear surface right from the beginning. Two illustrative simulations are presented to demonstrate the robustness and effectiveness of the introduced design. It is worthwhile noticing that the proposed approach can be applied to a wide variety of uncertain nonlinear control problems.