Spectral filters connecting high order systems

Three criteria are given to characterize when two linear dynamical systems have the same spectral structure (same finite and infinite elementary divisors). They are allowed to have different orders or sizes and their leading coefficient may be singular. One of the criteria uses generalized reversal...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 391; p. 125672
Main Authors Amparan, A., Marcaida, S., Zaballa, I.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.02.2021
Subjects
Filter
Finite elementary divisor
Infinite elementary divisor
Matrix polynomial
Spectral equivalence
93B25
Finite elementary divisor
Spectral equivalence
Filter
Infinite elementary divisor
15A54
Matrix polynomial
34K35
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Summary:Three criteria are given to characterize when two linear dynamical systems have the same spectral structure (same finite and infinite elementary divisors). They are allowed to have different orders or sizes and their leading coefficient may be singular. One of the criteria uses generalized reversal matrix polynomials, while the others rely on the existence of spectral filters. These are matrix polynomials which play a similar role to the change of bases for first order systems. A constructive procedure is presented to obtain spectral filters linking any two systems with the same spectral structure. Connections are made with the second-order systems decoupling problem.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2020.125672