New Results on the Composite Control of Singularly Perturbed Uncertain Linear Systems

We consider the problem of "stabilizing" uncertain, singularly perturbed, linear, time-varying, systems whose fast dynamics can be unstable. We propose a class of nonlinear composite controllers which assure global uniform ultimate boundedness of the trajectories of the closed loop system, provided the singular perturbation parameter is sufficiently small. These controllers consist of a fast controller which stabilizes the fast dynamics and a slow controller which yields the desired stability properties for the slow dynamics. We consider the structure of the fast controller to be simpler than structures previously proposed in the literature. To obtain these controllers, we first develop some new results for singularly perturbed systems under output feedback. In particular, it is shown that the matching assumption, which deals with the manner in which the uncertainties enter the system, and is made on the reduced-order system, is invariant under linear feedback of the fast variable.