Almost ISS property for feedback connected systems

TL;DR

This paper extends small-gain stability analysis by applying conditions over disjoint intervals and using density propagation to establish global stability in feedback interconnected systems.

Contribution

It introduces a novel approach combining disjoint interval analysis with density propagation to improve stability results for feedback systems.

Findings

Global stability can be achieved using multiple disjoint small-gain conditions.

Density propagation bridges gaps between intervals, enhancing stability guarantees.

The method improves upon previous results in feedback system analysis.

Abstract

Small-gain conditions used in analysis of feedback interconnections are contraction conditions which imply certain stability properties. Such conditions are applied to a finite or infinite interval. In this paper we consider the case, when a small-gain condition is applied to several disjunct intervals and use the density propagation condition in the gaps between these intervals to derive global stability properties for an interconnection. This extends and improves recent results from [1].