Output Feedback Control of a Class of Singularly Perturbed Uncertain Dynamical Systems

A class of uncertain dynamical systems, which can be decomposed into two coupled subsystems by means of a singular perturbation parameter ¿, is considered. The dimension of the output space is assumed to coincide with that of the reduced-order system (¿=0) state space. An output feedback strategy is first designed which guarantees that the feedback-controlled reduced-order system (¿=0) possesses a desired stability property P (taken here to be that of global uniform ultimate boundedness). The basic question then resolved is that of robustness of P with respect to singular perturbation. A value ¿*≫0 is determined such that, under output feedback control, the full-order system (¿≫0) possesses property P for all values ¿ (0,¿*).