# Positive Consensus of Directed Multi-agent Systems using Dynamic Output-feedback Control

## TL;DR

This paper develops a convex programming approach using LMIs and positive systems theory to achieve positive consensus in directed multi-agent systems with output-feedback protocols, ensuring states remain non-negative.

## Contribution

It introduces a novel convex algorithm for designing output-feedback protocols that guarantee positive consensus in directed multi-agent systems.

## Key findings

- Successfully designed protocols ensuring positive consensus
- States remain in the non-negative orthant during system evolution
- Numerical simulations validate theoretical results

## Abstract

This paper addresses the problem of positive consensus of directed multi-agent systems with observer-type output-feedback protocols. More specifically, directed graph is used to model the communication topology of the multi-agent system and linear matrix inequalities (LMIs) are used in the consensus analysis in this paper. Using positive systems theory and graph theory, a convex programming algorithm is developed to design appropriate protocols such that the multi-agent system is able to reach consensus with its state trajectory always remaining in the non-negative orthant. Finally, numerical simulations are given to illustrate the effectiveness of the derived theoretical results.