TY - JOUR
T1 - Compound matrices in systems and control theory
T2 - a tutorial
AU - Bar-Shalom, Eyal
AU - Dalin, Omri
AU - Margaliot, Michael
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.
PY - 2023/9
Y1 - 2023/9
N2 - 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.
AB - 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.
KW - Chaotic systems
KW - Contracting systems
KW - Cooperative systems
KW - Diagonal stability
KW - Hankel k-positive systems
KW - Positive systems
KW - Sign variation diminishing property
KW - Volume of parallelotopes
UR - http://www.scopus.com/inward/record.url?scp=85150072075&partnerID=8YFLogxK
U2 - 10.1007/s00498-023-00351-8
DO - 10.1007/s00498-023-00351-8
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AN - SCOPUS:85150072075
SN - 0932-4194
VL - 35
SP - 467
EP - 521
JO - Mathematics of Control, Signals, and Systems
JF - Mathematics of Control, Signals, and Systems
IS - 3
ER -