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arXiv · 2111.01419

The $k$-Compound of a Difference-Algebraic System

Ron Ofir·Michael Margaliot
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Abstract

The multiplicative and additive compounds of a matrix have important applications in geometry, linear algebra, and the analysis of dynamical systems. In particular, the $k$-compounds allow to build a $k$-compound dynamical system that tracks the evolution of $k$-dimensional parallelotopes along the original dynamics. This has recently found many applications in the analysis of non-linear systems described by ODEs and difference equations. Here, we introduce the $k$-compound system corresponding to a differential-algebraic system, and describe several applications to the analysis of discrete-time dynamical systems described by difference-algebraic equations.

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Ron Ofir, Michael Margaliot. 2021-11-02. The $k$-Compound of a Difference-Algebraic System. https://doi.org/10.1016/j.automatica.2023.111387

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