Displaying similar documents to “Incomplete matrix partial fraction expansion”

Proper feedback compensators for a strictly proper plant by polynomial equations

Frank Callier, Ferdinand Kraffer (2005)

International Journal of Applied Mathematics and Computer Science

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We review the polynomial matrix compensator equation X_lD_r + Y_lN_r = Dk (COMP), e.g. (Callier and Desoer, 1982, Kučera, 1979; 1991), where (a) the right-coprime polynomial matrix pair (N_r, D_r) is given by the strictly proper rational plant right matrix-fraction P = N_rD_r, (b) Dk is a given nonsingular stable closed-loop characteristic polynomial matrix, and (c) (X_l, Y_l) is a polynomial matrix solution pair resulting possibly in a (stabilizing) rational compensator given by the...

An equivalent matrix pencilfor bivariate polynomial matrices

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.

Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials

Irina Karelin, Leonid Lerer (2001)

International Journal of Applied Mathematics and Computer Science

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It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of...

New coprime polynomial fraction representation of transfer function matrix

Yelena M. Smagina (2001)

Kybernetika

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A new form of the coprime polynomial fraction C ( s ) F ( s ) - 1 of a transfer function matrix G ( s ) is presented where the polynomial matrices C ( s ) and F ( s ) 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 H B , H A B , ...