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arXiv · 2204.00676

Compound matrices in systems and control theory: a tutorial

Eyal Bar-Shalom·Omri Dalin·Michael Margaliot
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Abstract

The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a growing interest in applications of these compounds, and their generalizations, in systems and control theory. The goal of this tutorial paper is to provide a gentle and self-contained introduction to these topics with an emphasis on the geometric interpretation of the compounds, and to describe some of their recent applications including several non-trivial generalizations of positive systems, cooperative systems, contracting systems, and more.

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Eyal Bar-Shalom, Omri Dalin, Michael Margaliot. 2022-04-01. Compound matrices in systems and control theory: a tutorial. https://arxiv.org/abs/2204.00676

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