Linear matrix inequalities design approach for robust stabilization of uncertain nonlinear systems with perturbation based on optimally-tuned global sliding mode control

Abstract

This paper presents a novel global sliding mode control technique for the stabilization of a class of uncertain and nonlinear dynamic systems with perturbation. Using the Lyapunov stability theory and linear matrix inequality, some sufficient conditions are deduced to guarantee the asymptotic stabilization of the system states and to modify the robustness of the system. To improve the robust performance, an innovative reaching control law is designed to guarantee a chattering-free finite time performance under the uncertainty and nonlinearities and is optimally tuned using a modified random search algorithm. Simulation results are provided to show the effectiveness of the suggested technique.