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Generalized Lyapunov conditions for k-contraction: analysis and feedback design (2311.18388v2)

Published 30 Nov 2023 in eess.SY, cs.SY, and math.DS

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. 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.

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