Stability analysis of LTV systems via gain and phase

This paper considers the feedback stability analysis of infinite-dimensional discrete-time linear time-varying systems with combined gain and phase information. The framework considers a system to be a causal linear operator described by a lower triangular infinite-dimensional complex matrix. For r-sectorial operators, we first derive a sufficient condition for the invertibility of $I+AB$ using the gain and phase information. Finally, we use this invertibility criterion to give a sufficient condition for feedback stability of r-sectorial systems.