TY - JOUR
T1 - The k-compound of a difference–algebraic system
AU - Ofir, Ron
AU - Margaliot, Michael
N1 - Publisher Copyright:
© 2023 Elsevier Ltd
PY - 2024/1
Y1 - 2024/1
N2 - The multiplicative and additive compounds of a matrix have important applications in geometry, linear algebra, and the analysis of dynamical systems. In particular, the k-compounds allow to build a k-compound dynamical system that tracks the evolution of k-dimensional parallelotopes along the original dynamics. This has recently found many applications in the analysis of non-linear systems described by ODEs and difference equations. Here, we introduce the k-compound system corresponding to a difference–algebraic system, and describe several applications to the analysis of discrete-time dynamical systems.
AB - The multiplicative and additive compounds of a matrix have important applications in geometry, linear algebra, and the analysis of dynamical systems. In particular, the k-compounds allow to build a k-compound dynamical system that tracks the evolution of k-dimensional parallelotopes along the original dynamics. This has recently found many applications in the analysis of non-linear systems described by ODEs and difference equations. Here, we introduce the k-compound system corresponding to a difference–algebraic system, and describe several applications to the analysis of discrete-time dynamical systems.
KW - Drazin inverse
KW - Evolution of volumes
KW - Multiplicative compounds
KW - Wedge product
UR - http://www.scopus.com/inward/record.url?scp=85177555834&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2023.111387
DO - 10.1016/j.automatica.2023.111387
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AN - SCOPUS:85177555834
SN - 0005-1098
VL - 159
JO - Automatica
JF - Automatica
M1 - 111387
ER -