Unified treatment of robust stability conditions for discrete-time systems through an infinite matrix framework

This paper is motivated by the study on clarifying further relationship between the conventional lifting-free causal linear time-invariant (LTI) scaling and lifting-based noncausal linear periodically time-varying (LPTV) scaling approaches to robust stability analysis. To facilitate such a study, this paper gives the infinite matrix representation counterparts of the robust stability conditions in the separator-type robust stability theorems for these approaches. These counterparts lead to the idea of infinite-dimensional separators and provide us with a unified framework for studying the mutual relationship between these two approaches. This paper takes causal LTI and noncausal LPTV separators characterized by finite impulse response, which are respectively defined in the lifting-free and lifting-based frameworks, and compares them with respect to conservativeness of robust stability analysis by means of the unified framework. Through such a discussion, it is demonstrated that the unified framework can lead to a very comprehensible and intuitive study on the mutual relationship between causal LTI and noncausal LPTV scaling approaches.