Effects induced by noncausality of scaling on robust stability analysis of discrete-time periodically time-varying systems

This paper is concerned with robust stability analysis of discrete-time linear periodically time-varying (LPTV) systems. The well-known discrete-time lifting technique enables us to deal with LPTV systems as if they were linear time-invariant (LTI), and we can analyze the robust stability through the lifted (i.e., equivalent LTI) systems. Through such lifting treatment, the discrete-time causal/noncausal LPTV scaling can be naturally introduced to the robust stability analysis. This paper first investigates the effect of the noncausality in LPTV scaling by comparing causal and noncausal scaling, and explicitly discusses when and why the noncausality of the scaling induces the effectiveness in robust stability analysis of LPTV systems. The paper then discusses the influence of taking different timing in the lifting treatment in the analysis.