Controllability criteria for time-delay fractional systems with a retarded state

Beata Sikora

International Journal of Applied Mathematics and Computer Science (2016)

  • Volume: 26, Issue: 3, page 521-531
  • ISSN: 1641-876X

Abstract

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The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative U -controllability are established and proved. Numerical examples illustrate the obtained theoretical results.

How to cite

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Beata Sikora. "Controllability criteria for time-delay fractional systems with a retarded state." International Journal of Applied Mathematics and Computer Science 26.3 (2016): 521-531. <http://eudml.org/doc/286721>.

@article{BeataSikora2016,
abstract = {The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative U -controllability are established and proved. Numerical examples illustrate the obtained theoretical results.},
author = {Beata Sikora},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {fractional dynamical systems; controllability; delays in the state; constraints; pseudo-transition matrix; Caputo derivative},
language = {eng},
number = {3},
pages = {521-531},
title = {Controllability criteria for time-delay fractional systems with a retarded state},
url = {http://eudml.org/doc/286721},
volume = {26},
year = {2016},
}

TY - JOUR
AU - Beata Sikora
TI - Controllability criteria for time-delay fractional systems with a retarded state
JO - International Journal of Applied Mathematics and Computer Science
PY - 2016
VL - 26
IS - 3
SP - 521
EP - 531
AB - The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative U -controllability are established and proved. Numerical examples illustrate the obtained theoretical results.
LA - eng
KW - fractional dynamical systems; controllability; delays in the state; constraints; pseudo-transition matrix; Caputo derivative
UR - http://eudml.org/doc/286721
ER -

References

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