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The flow of contracting systems contracts 1dimensional 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 &#x2208;{1,...,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.

Serial interconnections of 1-contracting and 2-contracting systems