Stabilization and regulation of class of non-linear singularly perturbed discrete-time systems

A class of discrete-time nonlinear systems which are two-time-scale is treated. Using the singular perturbation theory in a systematic way, we present a mode-decoupling approach which yields two separate subsystems containing the slow and fast parts. Furthermore, a two-time-scale analysis and design procedure for stabilization and regulation is presented. The controllability and stabilizability invariance of the fast subsystem is shown and an asymptotic stabilizing composite feedback control is proposed. Finally, it is shown that the composite control produces a finite cost which tends to the optimal cost of a slow problem as the singular perturbation parameter tends to zero.