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Spectral filters connecting high order systems. (English) Zbl 1488.37017

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.

MSC:

37C30 Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc.
15A22 Matrix pencils
15A18 Eigenvalues, singular values, and eigenvectors

Software:

NLEVP
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Full Text: DOI

References:

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