Abstract
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.
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