Relationship between Noncausal Linear Periodically Time-Varying Scaling and Causal Linear Time-Invariant Scaling for Discrete-Time Systems

Abstract

AbstractIn this paper, we discuss the relationship between noncausal linear periodically time-varying (LPTV) scaling and causal linear time-invariant (LTI) scaling against discrete-time LTI closed-loop system. Noncausal LPTV scaling is naturally introduced via lifting technique, and can induce some frequency-dependent scaling in the lifting-free (i.e., usual) framework. However, it has not been clear what classes of noncausal LPTV scaling and causal LTI scaling have equivalent abilities in their respective frameworks. It is an important issue for sophisticating the theoretical base of noncausal LPTV scaling, and this paper studies such a relationship.