Compound matrices in systems and control theory: a tutorial

Eyal Bar-Shalom, Omri Dalin, Michael Margaliot*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)467-521
Number of pages55
JournalMathematics of Control, Signals, and Systems
Issue number3
StatePublished - Sep 2023


  • Chaotic systems
  • Contracting systems
  • Cooperative systems
  • Diagonal stability
  • Hankel k-positive systems
  • Positive systems
  • Sign variation diminishing property
  • Volume of parallelotopes


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