A Sufficient Condition for 2-Contraction of a Feedback Interconnection

• 成果类型: Article
• 署名作者: Ofir, Ron; Bullo, Francesco; Margaliot, Michael
• 署名单位: Tel Aviv University; 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.2025.3602711
• 发表日期: 2026
• 关键词: Contraction; compound; matrices; multistability; STABILITY; SYSTEM

摘要

We derive a new sufficient condition for 2-contraction of a feedback interconnection of two nonlinear dynamical systems. Our condition is based on, first, deriving new formulas for the 2-multiplicative [2-additive] compound of block matrices using block Kronecker products [sums], second, a hierarchical approach for proving standard contraction, and third, a network small-gain theorem for Metzler matrices. We demonstrate our results by deriving a simple sufficient condition for 2-contraction in a network of FitzHugh-Nagumo neurons.