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Noncausal Linear Periodically Time-Varying Scaling for Discrete-Time Systems

Yasuhiro Ohara
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 scaling is interpreted in the original time axis without
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 LTI scaling if it is interpreted in the context of lifting-free
treatment, and a possible advantage of noncausal LPTV scaling for
LTI plants is investigated from this viewpoint.
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