On Spectral Properties of Signed Laplacians With Connections to Eventual Positivity

• 成果类型: Article
• 署名作者: Chen, Wei; Wang, Dan; Liu, Ji; Chen, Yongxin; Khong, Sei Zhen; Basar, Tamer; Johansson, Karl H.; Qiu, Li
• 署名单位: Peking University; Peking University; Hong Kong University of Science & Technology; State University of New York (SUNY) System; Stony Brook University; University System of Georgia; Georgia Institute of Technology; University of Illinois System; University of Illinois Urbana-Champaign; Royal Institute of Technology; University of Melbourne; Lund University; University of Minnesota System; University of Minnesota Twin Cities; University of Hong Kong
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3008300
• 发表日期: 2021
• 页码: 2177-2190
• 关键词: n-port network; eventual positivity; signed Laplacians; spectral properties; Kron reduction

摘要

Signed graphs have appeared in a broad variety of applications, ranging from social networks to biological networks, from distributed control and computation to power systems. In this article, we investigate spectral properties of signed Laplacians for undirected signed graphs. We find conditions on the negative weights under which a signed Laplacian is positive semidefinite via the Kron reduction and multiport network theory. For signed Laplacians that are indefinite, we characterize their inertias with the same framework. Furthermore, we build connections between signed Laplacians, generalized M-matrices, and eventually exponentially positive matrices.