MATHEMATICAL ENGINEERING TECHNICAL REPORTS Periodically Weighted Model-Matching Problems with LPTV Controllers Formulated in Dual Lifted Forms

We consider two periodically weighted model-matching problems with regard to a discrete-time LTI plant by means of discrete-time linear periodically time-varying (LPTV) control. These two problems are formulated by projection operators and shown to be determined uniquely by corresponding LTI model-matching problems in which new free parameters arise from the periodically time-varying property of the controller. As a result, we can solve these problems approximately by using the usual LTI synthesis tools. The causality of the resulting LPTV controllers is guaranteed by a representation of a causal N -periodic system which we introduce as dual lifted forms. We also show an illustrative numerical example in which our proposing LPTV controller achieves superior performance to that of LTI controllers.