Positivity and stabilization of fractional 2D linear systems described by the Roesser model

Tadeusz Kaczorek; Krzysztof Rogowski

International Journal of Applied Mathematics and Computer Science (2010)

  • Volume: 20, Issue: 1, page 85-92
  • ISSN: 1641-876X

Abstract

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A new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2D Z-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation of a gain matrix is proposed and illustrated by a numerical example.

How to cite

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Tadeusz Kaczorek, and Krzysztof Rogowski. "Positivity and stabilization of fractional 2D linear systems described by the Roesser model." International Journal of Applied Mathematics and Computer Science 20.1 (2010): 85-92. <http://eudml.org/doc/207980>.

@article{TadeuszKaczorek2010,
abstract = {A new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2D Z-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation of a gain matrix is proposed and illustrated by a numerical example.},
author = {Tadeusz Kaczorek, Krzysztof Rogowski},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {positivity; stabilization; fractional systems; Roesser model; 2D systems},
language = {eng},
number = {1},
pages = {85-92},
title = {Positivity and stabilization of fractional 2D linear systems described by the Roesser model},
url = {http://eudml.org/doc/207980},
volume = {20},
year = {2010},
}

TY - JOUR
AU - Tadeusz Kaczorek
AU - Krzysztof Rogowski
TI - Positivity and stabilization of fractional 2D linear systems described by the Roesser model
JO - International Journal of Applied Mathematics and Computer Science
PY - 2010
VL - 20
IS - 1
SP - 85
EP - 92
AB - A new class of fractional 2D linear discrete-time systems is introduced. The fractional difference definition is applied to each dimension of a 2D Roesser model. Solutions of these systems are derived using a 2D Z-transform. The classical Cayley-Hamilton theorem is extended to 2D fractional systems described by the Roesser model. Necessary and sufficient conditions for the positivity and stabilization by the state-feedback of fractional 2D linear systems are established. A procedure for the computation of a gain matrix is proposed and illustrated by a numerical example.
LA - eng
KW - positivity; stabilization; fractional systems; Roesser model; 2D systems
UR - http://eudml.org/doc/207980
ER -

References

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