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The canonical Diophantine equations with applications. (English) Zbl 0568.93013
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:
93B25Algebraic theory of control systems
93C05Linear control systems
11D04Linear diophantine equations
15A23Factorization of matrices
93B15Realizability of systems from input-output data
93C35Multivariable systems, multidimensional control systems
15A33Matrices over special rings
93B10Canonical structure of systems