NONCAUSAL LINEAR PERIODICALLY TIME-VARYING SCALING FOR DISCRETE-TIME SYSTEMS

This paper is concerned with robust stability analysis of discrete-time systems. We first consider linear periodically time-varying (LPTV) nominal systems, for which we apply the discrete-time lifting to have their equivalent linear time-invariant (LTI) representations. Applying the conventional but general scaling approach to the LTI representations leads to the notion of noncausal LPTV scaling when the scaling is interpreted in the original time axis without lifting. Regarding this discrete-time noncausal LPTV scaling, we confirm its effectiveness over causal LPTV scaling and (causal) LTI scaling theoretically as well as with a numerical example. We next consider LTI nominal systems, for which we again apply noncausal LPTV scaling by regarding the LTI systems as a special case of LPTV systems and thus applying the discrete-time lifting in the same way as in the LPTV nominal systems. We then study the relationship of such an approach with the conventional LTI scaling applied directly to the LTI nominal systems without lifting treatment. In particular, we show that even static noncausal LPTV scaling yields dynamic (frequency-dependent) LTI scaling if it is interpreted in the context of lifting-free treatment, and an advantage of noncausal LPTV scaling for LTI nominal systems is investigated from this viewpoint. A numerical example is also provided that supports the advantage.