On the robustness of networks of heterogeneous semi-passive systems interconnected over directed graphs

TL;DR

This paper proves that networks of diverse semi-passive nonlinear systems interconnected over directed graphs with a spanning tree have bounded solutions, ensuring stability under specified conditions.

Contribution

It provides a formal proof of boundedness for heterogeneous semi-passive systems interconnected over directed graphs with minimal assumptions.

Findings

Solutions are bounded under semi-passivity and graph spanning tree conditions.

The proof applies to heterogeneous nonlinear autonomous systems.

Ensures stability of complex networked systems with directed interconnections.

Abstract

In this short note we provide a proof of boundedness of solutions for a network system composed of heterogeneous nonlinear autonomous systems interconnected over a directed graph. The sole assumptions imposed are that the systems are semi-passive [1] and the graph contains a spanning tree.