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Pré-Publication, Document De Travail Année : 2023

Generalized Lyapunov conditions for k-contraction: analysis and feedback design

Résumé

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 rely on matrix compounds. Our design-oriented conditions stem from a strong geometrical interpretation and establish a connection between kcontraction and p-dominance. Notably, these conditions are also necessary in the linear time-invariant framework. Leveraging on these findings, we propose a feedback design methodology for both the linear and the nonlinear scenarios.
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Dates et versions

hal-04300588 , version 1 (24-11-2023)

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Andreu Cecilia, Samuele Zoboli, Daniele Astolfi, Ulysse Serres, Vincent Andrieu. Generalized Lyapunov conditions for k-contraction: analysis and feedback design. 2023. ⟨hal-04300588⟩
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