Compound matrices in systems and control theory: a tutorial

Abstract

The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, graph theory, 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.