Robust stabilization of a class of singularly perturbed discrete bilinear systems

This paper presents two kinds of robust controllers for stabilizing singula rly perturbed discrete bilinear systems. The first one is an epsilon-depend ent controller that stabilizes the closed-loop system for all epsilon is an element of (0, epsilon(0)*), where epsilon(0)* is the prespecified upper b ound of the singular perturbation parameter. The second one is an epsilon-i ndependent controller, which is able to stabilize the system in the entire state space for all epsilon is an element of (0, epsilon*), where epsilon* is the exact upper epsilon-bound, The epsilon* fan be calculated by the cri tical stability criterion once the robust controller is determined. An exam ple is presented to illustrate the proposed schemes.