Robust stabilization for a class of nonlinear systems

This paper deals with globally asymptotical stabilization for nonlinear systems with structural uncertainty. Based on weak robust control Lyapunov functions (rclfs), a sufficient and necessary condition for the function to be a weak rclf is presented. Based on this condition, simply sufficient condition for the robustly globally asymptotical stabilization is deduced as well as an almost smooth state feedback. Next, it is shown that the globally asymptotical stabilization control is inverse optimal control associated with a meaningful cost function. Moreover, the inverse optimal control implies the optimal control whenever the level sets of the rclf match those of the optimal value function. The simulation shows the effectiveness of the method.