Robust control of nonlinear systems with convex input constraints and its application to the magnetic levitation system

In this paper, we consider the stabilization problem of nonlinear systems subject to convex input constraints. We modify the our previous results to be applicable for actual control problems. First, we design a robust stabilizing controller that guarantees a sector margin for convex input constrained nonlinear systems. To apply the proposed controller to the actual system, we have to compute the input which minimizes the time derivative of a local control Lyapunov function. We discuss how to obtain the minimizing input and clarify the condition when the minimizing input is analytically obtained. Finally, we apply the proposed method to the magnetic levitation system and confirm the effectiveness by experiments.