# A Passivity Analysis for Nonlinear Consensus on Digraphs

## TL;DR

This paper introduces a passivity-based framework for analyzing nonlinear consensus in directed network systems, enabling convergence guarantees for arbitrary digraphs with passive agents.

## Contribution

It develops a novel passivity analysis method that handles nonlinear, passive agents over arbitrary directed graphs, extending previous approaches.

## Key findings

- Ensures output convergence to the agreement submanifold.
- Applicable to nonlinear and passive agents in directed networks.
- Numerical examples validate the theoretical results.

## Abstract

This work presents a passivity-based analysis for the nonlinear output agreement problem in network systems over directed graphs. We reformulate the problem as a convergence analysis on the agreement submanifold. First, we establish how passivity properties of individual agents and controllers determine the passivity of their associated system relations. Building on this, we introduce the concept of submanifold-constrained passivity and develop a novel compensation theorem that ensures output convergence to the agreement submanifold. Unlike previous approaches, our approach can analyze the network system with arbitrary digraphs and any passive agents. We apply this framework to analyze the output agreement problem for network systems consisting of nonlinear and passive agents. Numerical examples support our results.