Global stabilization of systems containing a double integrator using a saturated linear controller

Abstract

In this paper, we present a Lyapunov function for systems containing a double integrator and with controller saturation. This Lyapunov function is composed of a positive-semidefinite quadratic term and an integral term. The main result provides a sufficient condition that guarantees a system with a double integrator can be globally stabilized by a saturating linear controller. For a triple-integrator system the saturated linear controller does not satisfy the sufficient condition, which agrees with the known result. Copyright © 1999 John Wiley & Sons, Ltd.