2021/11/02 by Ofir, Ron, Margaliot, Michael
#FOS: Electrical engineering #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.2111.01419
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 differential-algebraic system, and describe several applications to the analysis of discrete-time dynamical systems described by difference-algebraic equations.