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New results on ${H}_{\infty }$ control of discrete singularly perturbed systems. (English) Zbl 1179.93071
Summary: This paper studies the problem of ${H}_{\infty }$ control of discrete-time singularly perturbed systems. A new sufficient condition, which ensures the existence of state feedback controllers such that the resulting closed-loop system is asymptotically stable while satisfying a prescribed ${H}_{\infty }$ norm bound, is obtained. This condition is in terms of a linear matrix inequality, which is independent of the singular perturbation parameter. Furthermore, a new condition on searching for the allowable upper bound of the singular perturbation parameter is proposed, under which the discrete-time singularly perturbed system is asymptotically stable with an ${H}_{\infty }$ norm bound when the singular perturbation parameter is lower than this upper bound. In these derived conditions, the upper bound of the singular perturbation parameter is not required to be smaller than one. The reduced conservatism of our results is demonstrated via a numerical example.
##### MSC:
 93B36 ${H}^{\infty }$-control 93C70 Time-scale analysis and singular perturbations 15A39 Linear inequalities of matrices 93C55 Discrete-time control systems 93B52 Feedback control