2023/11/30 by Cecilia, Andreu, Zoboli, Samuele, Astolfi, Daniele +2
#Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2311.18388
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. Leveraging 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.