Eigensets of switching dynamical systems

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autore principale: Protasov, Vladimir
Natura: Preprint
Pubblicazione: 2026
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866911387201044480
author Protasov, Vladimir
author_facet Protasov, Vladimir
contents Reachability sets of linear switching dynamical systems (systems of ODE with time-dependent matrices that take values from a given compact set) are analysed. An eigenset is a non-trivial compact set M that possesses the following property: the closure of the set of points reachable by trajectories starting in M in time t is equal to exp(at)M. This concept introduced in a recent paper of E.Viscovini is an analogue of an eigenvector for compact sets of matrices. We prove the existence of eigensets, analyse their structure and properties, and find ``eigenvalues'' a for an arbitrary system. The question which compact sets, in particular, which convex sets and polyhedra, can be presented as eigensets of suitable systems, is studied.
format Preprint
id arxiv_https___arxiv_org_abs_2601_13990
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Eigensets of switching dynamical systems
Protasov, Vladimir
Dynamical Systems
Metric Geometry
Optimization and Control
Reachability sets of linear switching dynamical systems (systems of ODE with time-dependent matrices that take values from a given compact set) are analysed. An eigenset is a non-trivial compact set M that possesses the following property: the closure of the set of points reachable by trajectories starting in M in time t is equal to exp(at)M. This concept introduced in a recent paper of E.Viscovini is an analogue of an eigenvector for compact sets of matrices. We prove the existence of eigensets, analyse their structure and properties, and find ``eigenvalues'' a for an arbitrary system. The question which compact sets, in particular, which convex sets and polyhedra, can be presented as eigensets of suitable systems, is studied.
title Eigensets of switching dynamical systems
topic Dynamical Systems
Metric Geometry
Optimization and Control
url https://arxiv.org/abs/2601.13990