Generalized Lyapunov Conditions for K-Contraction: Analysis and Feedback Design

• 成果类型: Article
• 署名作者: Cecilia, Andreu; Zoboli, Samuele; Astolfi, Daniele; Serres, Ulysse; Andrieu, Vincent
• 署名单位: Universitat Politecnica de Catalunya; Centre National de la Recherche Scientifique (CNRS); Communaute d'universites et etablissements de Toulouse (Comue); Centre National de la Recherche Scientifique (CNRS); Universite Lyon 1; CNRS - Institute for Engineering & Systems Sciences (INSIS)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3605299
• 发表日期: 2026
• 关键词: convergence; THEOREM

摘要

Recently, the concept of $\mathit {k}$-contraction has been introduced as a promising generalization of contraction for dynamical systems. However, the study of $\mathit {k}$-contraction properties has faced significant challenges due to the reliance on complex mathematical objects called matrix compounds. As a result, related control design methodologies have yet to appear in the literature. In this article, we overcome existing limitations and propose new sufficient conditions for $\mathit {k}$-contraction which do not require matrix compounds computation. Notably, these conditions are also necessary in the linear time-invariant framework. Building on these findings, we propose a feedback design methodology for both the linear and the nonlinear scenarios which can be used to enforce $\mathit {k}$-contractivity properties on the closed-loop dynamics.