Global exponential stabilisation for nonlinear singularly perturbed systems

A globally exponentially stabilising composite feedback control is proposed for a general class of nonlinear singularly perturbed systems. 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 epsilon. Moreover, an upper bound epsilon* for the singular perturbation parameter epsilon, such that the main result still holds, is given. The composite Lyapunov function technique is adopted in this paper.