Robust stability analysis based on discrete-time FIR scaling

This paper is concerned with robust stability analysis of discrete-time linear time-invariant (LTI) systems via the separator-type robust stability theorem. It develops a framework for dealing with finite impulse response (FIR) scaling, as a special class of dynamic causal LTI scaling. FIR separators to be searched for in FIR scaling are dynamic in general, and they are much more difficult to directly deal with than static LTI separators. This paper resolves such a difficulty by exploiting some relevant results on the technique called noncausal linear periodically time-varying (LPTV) scaling and the well-known KYP lemma. The FIR scaling applied in this way enables us to analyze robust stability of closed-loop systems in a less conservative fashion than conventional static LTI scaling, and is shown to be more effective than μ-analysis through a numerical example.