Asymptotic stabilization of nonlinear systems with convex-polytope input constraints by continuous input

Abstract In this paper, we propose an asymptotic stabilization controller for a nonlinear system with a convex-polytope input constraint. Moreover, we show that the controller has inverse optimality in the domain of attraction. The controller input is continuous in the set in which the asymptotic stabilization is guaranteed. We consider the asymmetric constraint for zero-input, and this bias is adjusted by using a non-uniform scaling on each vertex point in the neighborhood of the origin. Therefore, the input cost of the inverse optimal performance functional is approximated by a quadratic function near the origin.