Robust stabilization of a class of singularly perturbed discrete bilinear systems

This paper presents two kinds of robust controllers for stabilizing singularly perturbed discrete bilinear systems. The first one is an epsilon-dependent controller that stabilizes the closed-loop system for all epsilon is an element of (0, epsilon(0)*), where epsilon(0)* is the prespecified upper bound of the singular perturbation parameter. The second one is an epsilon-independent 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 critical stability criterion once the robust controller is determined. An example is presented to illustrate the proposed schemes.