Serial interconnections of 1-contracting and 2-contracting systems

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.

References in corpus (4)

• A Generalization of Linear Positive Systems with Applications to Nonlinear Systems: Invariant Sets and the Poincaré-Bendixson Property
• Generalization of the multiplicative and additive compounds of square matrices and contraction in the Hausdorff dimension
• Serial interconnections of 1-contracting and 2-contracting systems
• Diagonal Stability of Discrete-time $k$-Positive linear Systems with Applications to Nonlinear Systems

Cited by in corpus (3)

• A sufficient condition for $k$-contraction of the series connection of two systems
• Serial interconnections of 1-contracting and 2-contracting systems
• $k$-Contraction in a Generalized Lurie System