Example Demonstrating the Application of Small-gain and Density Propagation Conditions for Interconnections

TL;DR

This paper illustrates how combining small-gain and density propagation conditions can ensure global stability in interconnected systems, especially when small-gain conditions alone fail, through a motivating example.

Contribution

It provides a practical example demonstrating the application of combined small-gain and density propagation conditions for stability analysis.

Findings

Density propagation can compensate when small-gain fails

Combined conditions ensure global stability

Example illustrates theoretical concepts effectively

Abstract

This work provides an example that motivates and illustrates theoretical results related to a combination of small-gain and density propagation conditions. Namely, in case the small-gain fails to hold at certain points or intervals the density propagation condition can be applied to assure global stability properties. We repeat the theoretical results here and demonstrate how they can be applied in the proposed example.