Global stabilization of non-linear singularly perturbed systems with fast actuators: exact design manifold approach

Abstract

In the integral manifold approach, the dynamical behaviour of a non-linear singularly perturbed system is captured geometrically by the rapid approach of the fast system states to the design manifold and remaining on the manifold thereafter. A globally stabilizing composite feedback control, i.e. the sum of a slow control and a fast control, is proposed for a general class of non-linear singularly perturbed systems with fast actuators such that the design manifold becomes an exact slow integral manifold and the trajectories of the closed-loop systems, starting from any initial states, are steered along the integral manifold to the origin, i.e. the original non-linear singularly perturbed system is globally asymptotically stabilized.