An Angular Approach to Stability Analysis of LTV Systems (December 2021)

In this paper, we introduce an angular approach to stability analysis of infinite-dimensional discrete-time linear time-varying (LTV) systems. The framework considers a linear system to be a linear (possibly unbounded) operator on that maps an input space to an output space. Based on the operator numerical range, a small phase theorem is established for stability analysis of feedback sectorial systems. Additionally, we further use the operator singular angle to give a sufficient condition for feedback stability of invertible systems.