Global exponential stabilization for a class of nonlinear singularly perturbed systems

Abstract

A globally exponentially (asymptotically) stabilizing composite feedback control is proposed in this paper for a general class of nonlinear multiple time-delay singularly perturbed systems in which the slow subsystem is exponentially stable in the absence of the fast states. The chosen design manifold under this composite feedback control becomes an exact integral manifold and the trajectories of the closed-loop systems are steered globally along the integral manifold to the origin exponentially, with some guaranteed convergence rate, for all sufficiently small singular perturbation parameter E.