LMI conditions for k-contraction analysis: a step towards design

Samuele Zoboli (1) , Andreu Cecilia (2) , Ulysse Serres (3) , Daniele Astolfi (3) , Vincent Andrieu (3)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 UPC - Universitat Politècnica de Catalunya = Université polytechnique de Catalogne [Barcelona]
3 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique

Recently, k-contraction has been proposed as a generalization of contraction properties for nonlinear timevariant systems. Existing tools for k-contraction analysis exploit complex mathematical tools known as matrix compounds. This prevented the development of related design methodologies. In this paper, we link k-contraction properties to partial stability analysis tools. This leads to new, design-oriented sufficient conditions for k-contraction analysis which do not involve matrix compounds. We also show that such sufficient conditions are necessary for the linear time-invariant framework. Finally, we compare our results to existing methods and highlight their advantages.

Domaines: Systèmes et contrôle [cs.SY]; Automatique; Systèmes dynamiques [math.DS]

Samuele Zoboli, Andreu Cecilia, Ulysse Serres, Daniele Astolfi, Vincent Andrieu. LMI conditions for k-contraction analysis: a step towards design. 62nd IEEE Conference on Decision and Control (2023), IEEE, Dec 2023, Singapore, Singapore. à paraître. ⟨hal-04304423⟩