Robust stabilization of a class of singularly perturbed discrete bilinear systems

Abstract

This paper presents two kinds of robust controllers for stabilizing singularly perturbed discrete bilinear systems. The first one is an /spl epsi/-dependent controller that stabilizes the closed-loop system for all /spl epsi//spl isin/(0, /spl epsi//sub 0/*), where /spl epsi//sub 0/* is the prespecified upper bound of the singular perturbation parameter. The second one is an /spl epsi/-independent controller, which is able to stabilize the system in the entire state space for all /spl epsi//spl isin/(0, /spl epsi/*), where /spl epsi/* is the exact upper /spl epsi/-bound. The /spl epsi/* can be calculated by the critical stability criterion once the robust controller is determined. An example is presented to illustrate the proposed schemes.