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] [element of] ([MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] 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] [element] (0, [Epsilon]*, where [Epsilon]*] is the exact upper [Epsilon]-bound. The [Epsilon]* can be calculated by the critical stability criterion once the robust controller is determined. An example is presented to illustrate the proposed schemes. Index Terms--Lyapunov equation, robust controller, singularly perturbed discrete bilinear systems, singular perturbation parameter.