H ∞ Control of Discrete-Time Singularly Perturbed Systems via Static Output Feedback

Abstract

This paper concentrates on $H_{\infty }$ control problems of discrete-time singularly perturbed systems via static output feedback. Two methods of designing an $H_{\infty }$ controller, which ensures that the resulting closed-loop system is asymptotically stable and meets a prescribed $H_{\infty }$ norm bound, are presented in terms of LMIs. Though based on the same matrix transformation, the two approaches are turned into different optimal problems. The first result is given by an $ϵ$-independent LMI, while the second result is related to $ϵ$. Furthermore, a stability upper bound of the singular perturbation parameter is obtained. The validity of the proposed two results is demonstrated by a numerical example.