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arXiv · 2104.00928

Serial interconnections of 1-contracting and 2-contracting systems

Ron Ofir·Michael Margaliot·Yoash Levron·Jean-Jacques Slotine
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Abstract

The flow of contracting systems contracts 1-dimensional polygons (i.e. lines) at an exponential rate. One reason for the usefulness of contracting systems is that many interconnections of contracting sub-systems yield an overall contracting system. A recent generalization of contracting systems is called $k$-contracting systems, where $k\in\{1,\dots,n\}$. The flow of such systems contracts $k$-dimensional polygons at an exponential rate, and in particular they reduce to contracting systems when $k=1$. Here, we analyze serial interconnections of $1$-contracting and $2$-contracting systems. We provide conditions guaranteeing that such interconnections have a well-ordered asymptotic behaviour, and demonstrate the theoretical results using several examples.

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Ron Ofir, Michael Margaliot, Yoash Levron, Jean-Jacques Slotine. 2021-04-02. Serial interconnections of 1-contracting and 2-contracting systems. https://doi.org/10.1109/cdc45484.2021.9682810

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