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Squaring down with simultaneous zeros cancellation by series compensation of a general (possibly polynomial or improper) linear system is investigated. All static and dynamical compensators that spotlight minimal McMillan degree are parameterized. This general result is particularized to get compensators that preserve the L2 or L∞ norm of the original system, either in continuous or discrete-time...
The problem of simultaneously squaring down and cancelling a specified part of the zeros of a completely general linear system by an invertible transformation is investigated from different standpoints. Various classes of solutions featuring minimal McMillan degree, unitary or J -- inner symmetry, either with respect to the imaginary axis or the unit circle are characterized in a realisation -- based...
Given a generalized system whose transfer matrix function may be improper or may be polynomial, we provide necessary and sufficient conditions under which a minimal factorization does exist. The conditions are formulated in terms of deflating subspaces of pencils related to a special type of realisation, called centered, which allows to efficiently cater for poles and/or zeroes at infinity.
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