Canonical forms of singular 1D and 2D linear systems

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 1, page 61-72
  • ISSN: 1641-876X

Abstract

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The paper consists of two parts. In the first part, new canonical forms are defined for singular 1D linear systems and a procedure to determine nonsingular matrices transforming matrices of singular systems to their canonical forms is derived. In the second part new canonical forms of matrices of the singular 2D Roesser model are defined and a procedure for determining realisations in canonical forms for a given 2D transfer function is presented. Necessary and sufficient conditions for the existence of a pair of nonsingular block diagonal matrices transforming the matrices of the singular 2D Roesser model to their canonical forms are established. A procedure for computing the pair of nonsingular matrices is presented.

How to cite

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Kaczorek, Tadeusz. "Canonical forms of singular 1D and 2D linear systems." International Journal of Applied Mathematics and Computer Science 13.1 (2003): 61-72. <http://eudml.org/doc/207624>.

@article{Kaczorek2003,
abstract = {The paper consists of two parts. In the first part, new canonical forms are defined for singular 1D linear systems and a procedure to determine nonsingular matrices transforming matrices of singular systems to their canonical forms is derived. In the second part new canonical forms of matrices of the singular 2D Roesser model are defined and a procedure for determining realisations in canonical forms for a given 2D transfer function is presented. Necessary and sufficient conditions for the existence of a pair of nonsingular block diagonal matrices transforming the matrices of the singular 2D Roesser model to their canonical forms are established. A procedure for computing the pair of nonsingular matrices is presented.},
author = {Kaczorek, Tadeusz},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {canonical form; transformation; singular; 2D Roesser model; 1D system; singular systems; 1D systems; discrete-time linear systems; realizations},
language = {eng},
number = {1},
pages = {61-72},
title = {Canonical forms of singular 1D and 2D linear systems},
url = {http://eudml.org/doc/207624},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Kaczorek, Tadeusz
TI - Canonical forms of singular 1D and 2D linear systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 1
SP - 61
EP - 72
AB - The paper consists of two parts. In the first part, new canonical forms are defined for singular 1D linear systems and a procedure to determine nonsingular matrices transforming matrices of singular systems to their canonical forms is derived. In the second part new canonical forms of matrices of the singular 2D Roesser model are defined and a procedure for determining realisations in canonical forms for a given 2D transfer function is presented. Necessary and sufficient conditions for the existence of a pair of nonsingular block diagonal matrices transforming the matrices of the singular 2D Roesser model to their canonical forms are established. A procedure for computing the pair of nonsingular matrices is presented.
LA - eng
KW - canonical form; transformation; singular; 2D Roesser model; 1D system; singular systems; 1D systems; discrete-time linear systems; realizations
UR - http://eudml.org/doc/207624
ER -

References

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