Stratification of full rank polynomial matrices
2013 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 439, no 4, 1062-1090 p.Article in journal (Refereed) Published
We show that perturbations of polynomial matrices of full normal-rank can be analyzed viathe study of perturbations of companion form linearizations of such polynomial matrices.It is proved that a full normal-rank polynomial matrix has the same structural elements asits right (or left) linearization. Furthermore, the linearized pencil has a special structurethat can be taken into account when studying its stratification. This yields constraintson the set of achievable eigenstructures. We explicitly show which these constraints are.These results allow us to derive necessary and sufficient conditions for cover relationsbetween two orbits or bundles of the linearization of full normal-rank polynomial matrices.The stratification rules are applied to and illustrated on two artificial polynomial matricesand a half-car passive suspension system with four degrees of freedom.
Place, publisher, year, edition, pages
Elsevier, 2013. Vol. 439, no 4, 1062-1090 p.
polynomial matrices, matrix pencils, linearization, perturbations, stratification, closure hierarchy, cover relations, StratiGraph
Computational Mathematics Computer Science
Research subject Numerical Analysis; Automatic Control
IdentifiersURN: urn:nbn:se:umu:diva-71154DOI: 10.1016/j.laa.2012.12.013OAI: oai:DiVA.org:umu-71154DiVA: diva2:622289
FunderSwedish Foundation for Strategic Research , A3 02:128