Non-Euclidean Contraction Theory for Monotone and Positive Systems

• 成果类型: Article
• 署名作者: Jafarpour, Saber; Davydov, Alexander; Bullo, Francesco
• 署名单位: University System of Georgia; Georgia Institute of Technology; University of California System; University of California Santa Barbara
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3224094
• 发表日期: 2023
• 页码: 5653-5660
• 关键词: Contraction theory; Interconnected systems; monotone systems; positive systems; stability theory

摘要

In this note, we study contractivity of monotone systems and exponential convergence of positive systems using non-Euclidean norms. We first introduce the notion of conic matrix measure as a framework to study stability of monotone and positive systems. We study properties of the conic matrix measures and investigate their connection with weak pairings and standard matrix measures. Using conic matrix measures and weak pairings, we characterize contractivity and incremental stability of monotone systems with respect to non-Euclidean norms. Moreover, we use conic matrix measures to provide sufficient conditions for exponential convergence of positive systems to their equilibria. We show that our framework leads to novel results on the contractivity of excitatory Hopfield neural networks and the stability of interconnected systems using nonmonotone positive comparison systems.