The $k$-Compound of a Difference-Algebraic System
Systems and Control
2025-05-20 v2 Systems and Control
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 -compounds allow to build a -compound dynamical system that tracks the evolution of -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 -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.
Cite
@article{arxiv.2111.01419,
title = {The $k$-Compound of a Difference-Algebraic System},
author = {Ron Ofir and Michael Margaliot},
journal= {arXiv preprint arXiv:2111.01419},
year = {2025}
}
Comments
Accepted for publication in Automatica