Yelena M. Smagina (2001)
Kybernetika
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A new form of the coprime polynomial fraction of a transfer function matrix is presented where the polynomial matrices and have the form of a matrix (or generalized matrix) polynomials with the structure defined directly by the controllability characteristics of a state- space model and Markov matrices , , ...
Luis Verde-Star (2017)
Special Matrices
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We show that an infinite lower Hessenberg matrix generates polynomial sequences that correspond to the rows of infinite lower triangular invertible matrices. Orthogonal polynomial sequences are obtained when the Hessenberg matrix is tridiagonal. We study properties of the polynomial sequences and their corresponding matrices which are related to recurrence relations, companion matrices, matrix similarity, construction algorithms, and generating functions. When the Hessenberg matrix is...
Miroslav Fiedler (1984)
Mathematica Slovaca
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Michael Šebek, Vladimír Kučera (1981)
Kybernetika
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Mohamed Boudellioua (2006)
International Journal of Applied Mathematics and Computer Science
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In this paper, we present a simple algorithm for the reduction of a given bivariate polynomial matrix to a pencil form which is encountered in Fornasini-Marchesini's type of singular systems. It is shown that the resulting matrix pencil is related to the original polynomial matrix by the transformation of zero coprime equivalence. The exact form of both the matrix pencil and the transformation connecting it to the original matrix are established.