Guaranteed Exponential Convergence for Uncertain Nonlinear Systems in the Presence of Singular Perturbations

Singularly perturbed systems described by ordinary differential equations are considered. The singular perturbation is characterized by a real non-negative system parameter ¿. For ¿=0, the system order is lower than that for ¿ ≫ 0. A basic result on the exponential convergence of singularly perturbed systems is presented. With this result, conditions are obtained which assume that a controller renders a singularly perturbed system exponentially convergent for all ¿ sufficiently small. These conditions are then utilized to obtain controllers for specific class of uncertain systems. The construction of these controllers requires only the information available on the uncertain reduced order system (¿ = 0). The results are illustrated by application to a simple nonlinear electromechanical system.