A note on separator-type robust stability theorem and well-posedness of linear time-invariant systems

This paper is concerned with the robust stability analysis of discrete-time linear time-invariant systems. Among approaches to such analysis is the one based on the separator-type robust stability theorem derived through the topological separation notion. This paper discusses a relationship between the well-posedness assumption and robust stability condition in this theorem, and shows that the former assumption is actually satisfied automatically and thus is redundant under the latter condition, provided that a mild assumption is satisfied about the uncertainty set. Relevant aspects are also discussed about well-posedness of uncertain systems including the continuous-time case.