A homotopy theorem for incremental stability

Abstract

A theorem is proved to verify incremental stability of a feedback system via a homotopy from a known incrementally stable system, making no assumptions on existence of an extended space, well-posedness or causality. A first corollary of that result is that incremental stability may be verified by separation of Scaled Relative Graphs, correcting two assumptions in [1, Theorem 2]. Necessity of this correction is demonstrated by example. A second corollary provides an incremental version of the classical IQC stability theorem. Finally it is shown how to relax assumptions of incremental boundeness on the operators.