A simple criterion for global exponential stabilizability of nonlinear multiple time-delay singularly perturbed systems

Abstract

A simple criterion for global exponential stability of a class of nonlinear multiple time-delay singularly perturbed systems, without the so-called ‘interconnection conditions’, is proposed in this paper. A globally exponentially stabilizing composite feedback control is also proposed such that the chosen design manifold becomes an exact integral manifold and the trajectories of the closed-loop systems, starting from any initial states, are steered along the integral manifold to the origin exponentially for all sufficiently small singular perturbation parameters e. The composite control technique is adopted in this paper.