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Realization and partial fractions. (English) Zbl 0767.93009

Beginning with the generalized version of P. A. Fuhrmann’s realization [Linear systems and operators in Hilbert space (1981; Zbl 0456.47001), §10], the authors generalize the pencil-form realization in the same way, i.e. based on partial-fraction decompositions with respect to arbitrary complementary parts of the extended complex plane which may correspond to stability and instability.
To connect the spaces used in the two methods, one adequately constructs an isomorphism between them, and several identities related to the McMillan degree [B. McMillan, Bell System Tech. J. 31, 217-279, 541-600 (1952)]. Finally, a new computational procedure is derived to obtain the partial-fraction decomposition of a rational matrix given in fractional form.
Reviewer: M.Voicu (Iaşi)

MSC:

93B15 Realizations from input-output data
93A99 General systems theory
93B25 Algebraic methods
93B40 Computational methods in systems theory (MSC2010)

Citations:

Zbl 0456.47001
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Full Text: DOI

References:

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