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 ε-dependent controller that stabilizes the closed-loop system for all ε∈(0, ε₀*), where ε₀ * is the prespecified upper bound of the singular perturbation parameter. The second one is an ε-independent controller, which is able to stabilize the system in the entire state space for all ε∈(0, ε*), where ε* is the exact upper ε-bound. The ε* can be calculated by the critical stability criterion once the robust controller is determined. An example is presented to illustrate the proposed schemes