2026-04-13T02:51:36Zhttps://recercat.cat/oai/requestoai:recercat.cat:2117/10492025-07-17T13:46:30Zcom_2072_1033col_2072_452950
Orbits of controllable and observable systems
Clotet Juan, Josep
García Planas, María Isabel
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
System theory
Algebras, Linear
Multilinear algebra
Matrices
Controllability
Observability
Lie group action
Orbits
Sistemes, Teoria de
Àlgebra lineal
Àlgebra multilineal
Matriu S, Teoria
Classificació AMS::15 Linear and multilinear algebra; matrix theory
Classificació AMS::93 Systems Theory; Control::93B Controllability, observability, and system structure
Let a time-invariant linear system $\left .\aligned \dot
x(t)&=Ax(t)+Bu(t)\\y(t)&=Cx(t)\endaligned \right \}$ corresponding to a
realization of a prescribed transfer function matrix can be represented
by triples of matrices $(A,B,C)$. The permitted transformations of
basis changes in the space state on the systems can be seen in the space
of triples of matrices as similarity equivalence. In this paper we give
a geometric characteriaztion of controllable and observable systems as
orbits under a Lie group action. As a corollary we obtain a lower bound
of the distance between a controllable and observable triple and the
nearest uncontrollable one.
1999
Article
https://hdl.handle.net/2117/1049
eng
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Open Access
Attribution-NonCommercial-NoDerivs 2.5 Spain
9
application/pdf