# 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

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topTadeusz 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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