Real Eventual Exponential Positivity of Complex-valued Laplacians: Applications to Consensus in Multi-agent Systems

Thumbnail Image

Files

2410.13700v1.pdf (298.54 KB)

Links to Files

http://arxiv.org/abs/2410.13700

Permanent Link

https://doi.org/10.48550/arXiv.2410.13700
 http://hdl.handle.net/11603/36995

Collections

UMBC Computer Science and Electrical Engineering Department
UMBC Faculty Collection

Author/Creator

Author/Creator ORCID

https://orcid.org/0000-0003-2537-2778

Date

2024-10-17

Type of Work

journal articles
preprints
Text

Department

Program

Citation of Original Publication

Rights

Attribution 4.0 International CC BY 4.0 Deed

Subjects

Electrical Engineering and Systems Science - Systems and Control
Computer Science - Systems and Control

Abstract

In this paper, we explore the property of eventual exponential positivity (EEP) in complex matrices. We show that this property holds for the real part of the matrix exponential for a certain class of complex matrices. Next, we present the relation between the spectral properties of the Laplacian matrix of an unsigned digraph with complex edge-weights and the property of real EEP. Finally, we show that the Laplacian flow system of a network is stable when the negated Laplacian admits real EEP. Numerical examples are presented to demonstrate the results.