Criterion for global exponential stabilisability of a class of nonlinear control systems via an integral manifold approach

Abstract

A simple necessary and sufficient criterion, without the so-called `interconnection conditions', for the global exponential stabilisability of a general class of nonlinear singularly perturbed systems is proposed in the paper. A globally exponentially stabilising 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 for all sufficiently small singular perturbation parameters. The composite Lyapunov function technique is adopted in the paper.