Work

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

Year: 2025

Type: article

Abstract: Recently, the concept of$k$-contraction has been introduced as a promising generalization of contraction for dynamical systems. However, the study of$k$-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 paper, we overcome existing limitations and propose new sufficient conditions for$k$-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$k$-contractivity properties on the closed-loop dynamics.

Source: IEEE Transactions on Automatic Control

DOI: 10.1109/tac.2025.3605299

Authors: Andreu Cecilia, Samuele Zoboli, Daniele Astolfi, Ulysse Serres, Vincent Andrieu