Eigensets of switching dynamical systems
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911387201044480 |
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| 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 |