A combination of small-gain and density propagation inequalities for stability analysis of networked systems

TL;DR

This paper introduces a novel approach combining small-gain and density propagation inequalities to analyze the stability of large-scale interconnected nonlinear systems where traditional small-gain conditions fail globally.

Contribution

It presents a new method for stability analysis of complex networks by integrating small-gain and density propagation techniques, extending applicability beyond classical conditions.

Findings

Proves almost input-to-state stability of the network

Demonstrates effectiveness of combined inequalities in stability analysis

Extends stability analysis methods to systems where small-gain does not hold globally

Abstract

In this paper, the problem of stability analysis of a large-scale interconnection of nonlinear systems for which the small-gain condition does not hold globally is considered. A combination of the small-gain and density propagation inequalities is employed to prove almost input-to-state stability of the network.