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Computation of a canonical form for neutral delay-diﬀerential systems

Boudellioua M. S.

Control and Cybernetics

2015

Vol. 44, no. 3

357--368

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.

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

Boudellioua M. S.

Control and Cybernetics

2013

Vol. 42, no. 2

543--551

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.