Infinite matrix representations of robust stability conditions for discrete-time systems

This paper is motivated by the study on clarifying further relationship between the conventional lifting-free scaling and lifting-based noncausal linear periodically time-varying 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. Through the derivation and comparison of explicit forms of infinite-dimensional separators in these two approaches, it is demonstrated that the infinite matrix representation framework leads to a very comprehensible and intuitive study on the mutual relationship between these approaches.