Geometric classification of monogenic subspaces and uniparametric linear control systems
We present a geometric approach to the classification of monogenic invariant subspaces, alternative to the classical algebraic one, which allows us to obtain several matricial canonical forms for each class. Some applications are derived: canonical coordinates of a vector with regard to an endomorph...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/27960 |
| Acceso en línea: | https://hdl.handle.net/2117/27960 https://dx.doi.org/10.1080/03081087.2014.973874 |
| Access Level: | acceso abierto |
| Palabra clave: | Linear systems Matrices--Mathematical models endomorphism invariant subspaces monogenic subspaces marked matrices uniparametric control system bimodal dynamical system Sistemes lineals Matrius (Matemàtica) Classificació AMS::15 Linear and multilinear algebra matrix theory Classificació AMS::93 Systems Theory Control::93B Controllability, observability, and system structure Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | We present a geometric approach to the classification of monogenic invariant subspaces, alternative to the classical algebraic one, which allows us to obtain several matricial canonical forms for each class. Some applications are derived: canonical coordinates of a vector with regard to an endomorphism, and a canonical form for uniparametric linear control systems, not necessarily controllable, with regard to linear changes of state variables. Moreover, the pointwise construction can be extended to differentiable families of changes of basis when differentiable families of equivalent monogenic subspaces are considered. |
|---|