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Zbl 0568.93013
Wolovich, W.A.; Antsaklis, P.J.
The canonical Diophantine equations with applications. (English)
[J] SIAM J. Control Optimization 22, 777-787 (1984). ISSN 0363-0129; ISSN 1095-7138/e

A fundamental relationship between appropriate pairs of polynomial matrices is presented. This relationship, termed canonical Diophantine equations, can be used to resolve a number of standard polynomial matrix problems. Here, the general Diophantine equation is constructively resolved in a unique minimal way; in addition, prime canonical factorizations of a system transfer matrix are derived from knowledge of any dual factorization.

MSC 2000:: *93B25 Algebraic theory of control systems
93C05 Linear control systems
11D04 Linear diophantine equations
15A23 Factorization of matrices
93B15 Realizability of systems from input-output data
93C35 Multivariable, multidimensional control systems
15A33 Matrices over special rings
93B10 Canonical structure of systems

Keywords: polynomial matrices; canonical Diophantine equations; prime canonical factorizations; system transfer matrix

Cited in: Zbl 0666.93073

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