Local pinning of networks of multi-agent systems with transmission and pinning delays

TL;DR

This paper analyzes the stability of multi-agent networks with local pinning control considering transmission and pinning delays, providing conditions for stability and methods for verification through simulations.

Contribution

It introduces new stability conditions for networks with delays and pinning strategies, including single-node pinning and perturbation analysis for different pinning strengths.

Findings

Derived sufficient stability conditions for delayed networks

Proposed numerical algorithms for stability verification

Validated results with simulation examples

Abstract

We study the stability of networks of multi-agent systems with local pinning strategies and two types of time delays, namely the transmission delay in the network and the pinning delay of the controllers. Sufficient conditions for stability are derived under specific scenarios by computing or estimating the dominant eigenvalue of the characteristic equation. In addition, controlling the network by pinning a single node is studied. Moreover, perturbation methods are employed to derive conditions in the limit of small and large pinning strengths.Numerical algorithms are proposed to verify stability, and simulation examples are presented to confirm the efficiency of analytic results.