An LMI Formulation of Small-Gain Theorems for 2-Contraction of Nonlinear Interconnected Systems

• 成果类型: Article
• 署名作者: Angeli, David; Martini, Davide; Innocenti, Giacomo; Tesi, Alberto
• 署名单位: Imperial College London; University of Florence
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3558142
• 发表日期: 2025
• 页码: 6214-6221
• 关键词: Jacobian matrices; Compounds; Additives; Stability criteria; Interconnected systems; vectors; Symmetric matrices; Matrix decomposition; Perturbation methods; Linear systems; Contraction theory; multistability; nonlinear feedback systems; small-gain theorems

摘要

This article introduces small-gain sufficient conditions for 2-contraction of feedback interconnected systems, on the basis of individual gains of suitable subsystems arising from a modular decomposition of the second additive compound matrix variational equation. The gains are computed through the solution of suitable linear matrix inequality conditions. The criterion applies even to cases when individual subsystems might fail to be contractive, thanks to the extra margin of contraction afforded by the second additive compound matrix. One example is provided to illustrate the theory and show its degree of conservatism and scope of applicability.