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${H}_{\infty }$ state feedback control for discrete singular systems. (English) Zbl 0988.93026
Summary: This note deals with the problem of state feedback ${H}_{\infty }$ control for discrete singular systems. It is not assumed that the singular system under consideration is necessarily regular. The problem we address is the design of a state feedback controller such that the resulting closed-loop system is not only regular, causal, and stable, but also satisfies a prescribed ${H}_{\infty }$-norm-bound condition. In terms of certain matrix inequalities, a necessary and sufficient condition for the solution to this problem is obtained, and a suitable state feedback-control law is also given.
MSC:
 93B36 ${H}^{\infty }$-control 93C55 Discrete-time control systems