Global Uniform Ultimate Boundedness of Semi-Passive Systems Interconnected over Directed Graphs

TL;DR

This paper proves that interconnected semi-passive nonlinear systems over directed graphs are globally uniformly ultimately bounded, ensuring solutions remain bounded over time in networked control systems.

Contribution

It establishes the global uniform ultimate boundedness of solutions for heterogeneous semi-passive systems interconnected over directed graphs with a spanning tree.

Findings

Solutions are globally uniformly ultimately bounded.

Solutions are globally uniformly bounded.

Applicable to heterogeneous nonlinear networked systems.

Abstract

We analyse the solutions of networked heterogeneous nonlinear systems. We assume that the closed-loop interconnected systems form a network with an underlying connected directed graph that contains a directed spanning tree. For these systems, we establish global uniform ultimate boundedness of the solutions, under the assumption that each agent's dynamics defines a semi-passive. As a corollary, we also establish global uniform global boundedness of the solutions.