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Synthesis of robust performance controllers based on discrete-time noncausal linear periodically time-varying scaling

Abstract This paper is concerned with the discrete-time noncausal linear periodically time-varying (LPTV) scaling technique. It is defined through the discrete-time lifting, and it has been shown that even static noncausal LPTV scaling induces some frequency-dependent scaling when it is interpreted in the context of lifting-free treatment. It has been also shown that this feature together with the fact that the uncertainties come to be dealt with in their lifted forms leads to an effective method for robust stability analysis. This paper shows that noncausal LPTV scaling is effective also in controller design. More precisely, we study the periodic robust performance controller synthesis problem, and discuss how the properties of noncausal LPTV scaling lead to the performance improvement when the period of the controller is increased.