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Bounding the distance of a controllable system to an uncontrollable one
dc.contributor.author | Clotet Juan, Josep |
dc.contributor.author | García Planas, María Isabel |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2007-05-28T16:24:17Z |
dc.date.available | 2007-05-28T16:24:17Z |
dc.date.created | 1998 |
dc.date.issued | 1998 |
dc.identifier.uri | http://hdl.handle.net/2117/1050 |
dc.description.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 $(A,B)$. |
dc.format.extent | 18 |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 2.5 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/2.5/es/ |
dc.subject.lcsh | Algebras, Linear |
dc.subject.lcsh | Multilinear algebra |
dc.subject.lcsh | Matrices |
dc.subject.lcsh | System theory |
dc.subject.other | Linear Systems |
dc.subject.other | Controllability measure |
dc.subject.other | Distance to uncontrollable |
dc.title | Bounding the distance of a controllable system to an uncontrollable one |
dc.type | Article |
dc.subject.lemac | Àlgebra lineal |
dc.subject.lemac | Àlgebra multilineal |
dc.subject.lemac | Matriu S, Teoria |
dc.subject.lemac | Sistemes, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.subject.ams | Classificació AMS::15 Linear and multilinear algebra; matrix theory |
dc.subject.ams | Classificació AMS::93 Systems Theory; Control::93B Controllability, observability, and system structure |
dc.rights.access | Open Access |
local.personalitzacitacio | true |
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