k-contraction analysis for discrete-time systems

The definition of k-contraction promises a useful generalization of the classical notion of contraction for dynamical systems. However, most of the k-contraction literature focuses on continuous-time systems. In this work, we derive conditions for k-contractivity of discrete-time dynamics. Our first...

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Bibliographic Details
Published in:IFAC-PapersOnLine 2024, Vol.58 (21), p.144-149
Main Authors: Zoboli, Samuele, Cecilia, Andreu
Format: Article
Language:English
Subjects:
Compound matrices
Contraction
Discrete-time systems
Nonlinear systems
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Summary:The definition of k-contraction promises a useful generalization of the classical notion of contraction for dynamical systems. However, most of the k-contraction literature focuses on continuous-time systems. In this work, we derive conditions for k-contractivity of discrete-time dynamics. Our first result follows traditional lines for k-contraction analysis, and provides Lyapunov-like sufficient conditions based on matrix compounds and state-dependent metrics. However, our subsequent results avoid the complexities related to matrix compounds. Inspired by recent findings in the context of k-contraction for continuous-time systems, we provide conditions on the system's dynamics that rely on generalized Lyapunov inequalities and quadratic cone fields. The proposed conditions are also shown to be necessary for linear time-invariant systems.
ISSN:2405-8963
2405-8963
DOI:10.1016/j.ifacol.2024.10.161