Compound matrices in systems and control theory

TL;DR

This paper introduces compound matrices and their applications in systems and control theory, emphasizing geometric interpretation and recent developments in the field.

Contribution

It provides a comprehensive tutorial on compound matrices, highlighting their geometric meaning and surveying recent applications in systems and control theory.

Findings

Clarifies the geometric interpretation of compound matrices

Summarizes recent applications in nonlinear systems analysis

Highlights the importance of compounds in control theory

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. This tutorial paper provides a gentle introduction to these topics with an emphasis on the geometric interpretation of the compounds, and surveys some of their recent applications.