An Individual-Delay-Reflected Generalized Consensus Analysis for Multi-Agent Systems with Heterogeneous Time-Varying Delays

TL;DR

This paper proposes a new consensus analysis method for multi-agent systems with heterogeneous time-varying delays, reducing conservatism and allowing adjustable computational complexity.

Contribution

It introduces an individual-delay-reflected generalized consensus approach using a novel Lyapunov-Krasovskii functional tailored for heterogeneous delays.

Findings

Reduces conservatism in consensus analysis.

Demonstrates effectiveness through numerical examples.

Allows adjustable complexity via N-dependent inequality.

Abstract

In multi-agent systems, heterogeneous time delays exist for all agents because of the difference in communication environments. Therefore, the consensus analysis of a system considering a homogeneous time-varying delay among all agents results in conservatism. In this study, an individual-delay-reflected generalized consensus is proposed for multi-agent systems with heterogeneous time-varying delays with various bounds. To reflect heterogeneous time-varying delays, the proposed Lyapunov-Krasovskii functional is constructed by dividing the integral term into intervals containing heterogeneous delays and considering augmented vectors with delay states and integral states. Furthermore, by adding zero equality conditions, conservatism is reduced. N-dependent generalized integral inequality is used to allow the user to adjust the computational complexity. Numerical examples demonstrate a reduction in conservatism with the proposed consensus criterion.