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Computation of a canonical form for neutral delay-diﬀerential systems

Boudellioua M. S.

Control and Cybernetics

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2015

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Vol. 44, no. 3

357--368

EN

In this paper, symbolic computation techniques are used to obtain a canonical form for polynomial matrices arising from linear delay-diﬀerential systems of the neutral type. The canonical form can be regarded as an extension of the companion form, often encountered in the theory of linear systems, described by ordinary diﬀerential equations. Using the Smith normal form, the exact connection between the original polynomial matrix and the reduced canonical form is set out. An example is given to illustrate the computational aspects involved.

2

Further results on the equivalence to Smith form of multivariate polynomial matrices

Boudellioua M. S.

Control and Cybernetics

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2013

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Vol. 42, no. 2

543--551

EN

Multivariate polynomial matrices arise from the treatment of linear systems of partial differential equations, delay-differential equations or multidimensional discrete equations. In this paper we generalize some of the results obtained for the equivalence to the Smith normal form for a class of multivariate polynomial matrices.

3

Equivalence and reduction of delay-differential systems

Boudellioua M. S.

International Journal of Applied Mathematics and Computer Science

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2007

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Vol. 17, no 1

15-22

EN

A new direct method is presented which reduces a given high-order representation of a control system with delays to a firstorder form that is encountered in the study of neutral delay-differential systems. Using the polynomial system description (PMD) setting due to Rosenbrock, it is shown that the transformation connecting the original PMD with the first-order form is Fuhrmann’s strict system equivalence. This type of system equivalence leaves the transfer function and other relevant structural properties of the original system invariant.

4

An equivalent matrix pencil for bivariate polynomial matrices

Boudellioua M. S.

International Journal of Applied Mathematics and Computer Science

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2006

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Vol. 16, no 2

175-181

EN

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.