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...

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Detalles Bibliográficos
Autores: Compta Creus, Albert|||0000-0003-2388-3283, Ferrer Llop, Josep|||0000-0003-3380-231X
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
Descripción
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.