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When is a controller optimal in the sense of H-infinity loop-shaping?

## J. Feng and M.C. Smith

## Abstract

In this paper we characterize the controllers which are possible solutions of a certain H-infinity control design problem. The problem considered is the optimal robustness problem for (weighted) normalized coprime factor/gap metric uncertainty, which is the basis for the Glover-McFarlane H-infinity loop-shaping design method. Given a plant P and a corresponding controller C we ask if C can be obtained from the optimization procedure for some choice of weighting function. This paper considers single-input/single-output systems and gives necessary and sufficient conditions for optimality which involve right half plane pole/zero counts and a certain winding number test based on the Nyquist diagram of PC. The results give a characterization of this class of H-infinity-optimal designs in the language of classical control.