Bounding the distance of a controllable system to an uncontrollable one
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Inclou dades d'ús des de 2022
Cita com:
hdl:2117/1050
Tipus de documentArticle
Data publicació1998
Condicions d'accésAccés obert
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Reconeixement-NoComercial-SenseObraDerivada 2.5 Espanya
Abstract
Let $(A,B)$ be a pair of matrices representing a time-invariant linear
system $\dot x(t)=Ax(t)+Bu(t)$ under block-similarity equivalence.
In this paper we measure the distance between a controllable pair of
matrices $(A,B)$ and the nearest uncontrollable one.
A bound is obtained in terms of singular values of the controllability
matrix $C(A,B)$ associated to the pair. This bound is not simply based
on the smallest singular value of $C(A,B)$ contrary to what one may
expect.
Also a lower bound is obtained using geometrical techniques expressed
in terms of the singular values of a matrix representing the tangent
space of the orbit of the pair $(A,B)$.
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