Robustness of a Class of Feedback-Controlled Uncertain Nonlinear Systems in the Presence of Singular Perturbations

A class of uncertain, singularly perturbed, nonlinear, control systems described by ordinary differential equations is considered. The uncertainties are characterized deterministically; the singular perturbation is characterized by a real non-negative system parameter ¿. For ¿ = 0, the system order is lower than that for ¿ ≫ 0. Based only on information available on the uncertain reduced-order system (¿ = 0), controllers are presented which assure that the behavior of the feedback controlled reduced-order system is close to that of global uniform asymptotic stability about zero. Subject to the same controllers, the full-order system (¿ ≫ 0) has the same qualitative behavior, provided ¿ ≪ ¿*, where ¿* ≫ 0 can be computed from the available information. The results are illustrated by application to a simple electromechanical system.