An algebraic stability test for fractional order time delay systems
In this study, an algebraic stability test procedure is presented for fractional order time delay systems. This method is based on the principle of eliminating time delay. The stability test of fractional order systems cannot be examined directly using classical methods such as Routh-Hurwitz, becaus...
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Balikesir University
2020-01-01
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doaj-61ca8bb67cf34598a4a5888c84cf16142021-03-09T02:14:13ZengBalikesir UniversityAn International Journal of Optimization and Control: Theories & Applications 2146-09572146-57032020-01-0110110.11121/ijocta.01.2020.00803An algebraic stability test for fractional order time delay systemsMünevver Mine Özyetkin0Dumitru Baleanu1Aydın Adnan Menderes UniversityCankaya University, Department of Mathematics, Faculty of SciencesIn this study, an algebraic stability test procedure is presented for fractional order time delay systems. This method is based on the principle of eliminating time delay. The stability test of fractional order systems cannot be examined directly using classical methods such as Routh-Hurwitz, because such systems do not have analytical solutions. When a system contains the square roots of s, it is seen that there is a double value function of s. In this study, a stability test procedure is applied to systems including sqrt(s) and/or different fractional degrees such as s^alpha where 0 < ? < 1, and ? include in R. For this purpose, the integer order equivalents of fractional order terms are first used and then the stability test is applied to the system by eliminating time delay. Thanks to the proposed method, it is not necessary to use approximations instead of time delay term such as Pade. Thus, the stability test procedure does not require the solution of higher order equations. http://www.ijocta.org/index.php/files/article/view/803Fractional order systemspproximationTime delayStability |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Münevver Mine Özyetkin Dumitru Baleanu |
spellingShingle |
Münevver Mine Özyetkin Dumitru Baleanu An algebraic stability test for fractional order time delay systems An International Journal of Optimization and Control: Theories & Applications Fractional order systems pproximation Time delay Stability |
author_facet |
Münevver Mine Özyetkin Dumitru Baleanu |
author_sort |
Münevver Mine Özyetkin |
title |
An algebraic stability test for fractional order time delay systems |
title_short |
An algebraic stability test for fractional order time delay systems |
title_full |
An algebraic stability test for fractional order time delay systems |
title_fullStr |
An algebraic stability test for fractional order time delay systems |
title_full_unstemmed |
An algebraic stability test for fractional order time delay systems |
title_sort |
algebraic stability test for fractional order time delay systems |
publisher |
Balikesir University |
series |
An International Journal of Optimization and Control: Theories & Applications |
issn |
2146-0957 2146-5703 |
publishDate |
2020-01-01 |
description |
In this study, an algebraic stability test procedure is presented for fractional order time delay systems. This method is based on the principle of eliminating time delay. The stability test of fractional order systems cannot be examined directly using classical methods such as Routh-Hurwitz, because such systems do not have analytical solutions. When a system contains the square roots of s, it is seen that there is a double value function of s. In this study, a stability test procedure is applied to systems including sqrt(s) and/or different fractional degrees such as s^alpha where 0 < ? < 1, and ? include in R. For this purpose, the integer order equivalents of fractional order terms are first used and then the stability test is applied to the system by eliminating time delay. Thanks to the proposed method, it is not necessary to use approximations instead of time delay term such as Pade. Thus, the stability test procedure does not require the solution of higher order equations.
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topic |
Fractional order systems pproximation Time delay Stability |
url |
http://www.ijocta.org/index.php/files/article/view/803 |
work_keys_str_mv |
AT munevvermineozyetkin analgebraicstabilitytestforfractionalordertimedelaysystems AT dumitrubaleanu analgebraicstabilitytestforfractionalordertimedelaysystems AT munevvermineozyetkin algebraicstabilitytestforfractionalordertimedelaysystems AT dumitrubaleanu algebraicstabilitytestforfractionalordertimedelaysystems |
_version_ |
1724228231052132352 |