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Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2020 / Cilt: 10 - Sayı: 1

An algebraic stability test for fractional order time delay systems

Münevver Mine ÖZYETKİN
Dumitru BALEANU
Pages
94–103
Publication Date
2022-10-11
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Thus, the stability test procedure does not require the solutionof higher order equations.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, an algebraic stability test procedure is presented for fractionalorder time delay systems.
📊
Key Findings & Data:In this study, a stabilitytest procedure is applied to systems including ps and/or different fractionaldegrees such as s where 0 < α < 1, and αǫR.
💡
Conclusion & Impact:Thus, the stability test procedure does not require the solutionof higher order equations.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, an algebraic stability test procedure is presented for fractionalorder time delay systems. This method is based on the principle of eliminatingtime delay. The stability test of fractional order systems cannot be examineddirectly using classical methods such as Routh-Hurwitz, because such systemsdo not have analytical solutions. When a system contains the square roots ofs, it is seen that there is a double value function of s. In this study, a stabilitytest procedure is applied to systems including ps and/or different fractionaldegrees such as s where 0 < α < 1, and αǫR. For this purpose, the integerorder equivalents of fractional order terms are first used and then the stabilitytest is applied to the system by eliminating time delay. Thanks to the proposedmethod , it is not necessary to use approximations instead of time delay termsuch as Pad´e. Thus, the stability test procedure does not require the solutionof higher order equations.

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Cite This Article

ÖZYETKİN, M. M., BALEANU, D. (2022). An algebraic stability test for fractional order time delay systems. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 10 - Sayı: 1, 94–103. https://ajindex.com/articles/440580

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