2026-04-16T23:04:56Zhttps://recercat.cat/oai/requestoai:recercat.cat:2117/10482025-07-17T04:42:40Zcom_2072_1033col_2072_452950
Bounding the distance of a controllable and observable system to an uncontrollable or unobservable one
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
Algebras, Linear
Multilinear algebra
Matrices
System theory
Linear Systems
Controllability measure
Observability measure
Distance to uncontrollable and unobservable
Àlgebra lineal
Àlgebra multilineal
Matriu S, Teoria
Sistemes, Teoria de
Classificació AMS::15 Linear and multilinear algebra; matrix theory
Classificació AMS::93 Systems Theory; Control::93B Controllability, observability, and system structure
Let $(A,B,C)$ be a triple of matrices representing a time-invariant
linear system $\left .\aligned \dot
x(t)&=Ax(t)+Bu(t)\\y(t)&=Cx(t)\endaligned \right \}$ under similarity
equivalence, corresponding to a realization of a prescribed transfer
function matrix.
In this paper we measure the distance between a irreducible realization,
that is to say a controllable and observable triple of matrices $(A,B,C)$
and the nearest reducible one that is to say uncontrollable or unobservable
one.
Different upper bounds are obtained in terms of singular values of the
controllability matrix $C(A,B,C)$, observability matrix $O(A,B,C)$ and
controllability and observability matrix $CO(A,B,C)$ associated to the
triple.
1999
Article
https://hdl.handle.net/2117/1048
eng
http://creativecommons.org/licenses/by-nc-nd/2.5/es/
Open Access
Attribution-NonCommercial-NoDerivs 2.5 Spain
11
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