Journals / Manas Journal of Engineering / 2020 / Cilt: 8 - Sayı: 1

A new approach on the stability of fractional singular systems with time-varying delay

Pages
59–67
Publication Date
2022-10-19
DOI
—
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AI Summary & Key Takeaways

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

The theoretical results obtained in this research contribute to existingones in the literature.

📌 3 Key Takeaways

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Objective & Hypothesis:In this research article, we discussed the asymptotic stability of fractional singular systems withRiemann–Liouville (RL) derivative and constructed some sufficient conditions.
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Key Findings & Data:Finally, we presented twosimple numerical examples with their simulations to demonstrate the effectiveness and benefitsof the proposed method.
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Conclusion & Impact:The theoretical results obtained in this research contribute to existingones in the literature.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this research article, we discussed the asymptotic stability of fractional singular systems withRiemann–Liouville (RL) derivative and constructed some sufficient conditions. The proposedstability criteria are based upon the linear matrix inequalities (LMIs) approach, which can beeasily checked using meaningful Lyapunov-Krasovskii functionals. Finally, we presented twosimple numerical examples with their simulations to demonstrate the effectiveness and benefitsof the proposed method. The theoretical results obtained in this research contribute to existingones in the literature.

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Cite This Article

Altun, Y. (2022). A new approach on the stability of fractional singular systems with time-varying delay. Manas Journal of Engineering, Cilt: 8 - Sayı: 1, 59–67. https://ajindex.com/articles/578015

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References (1)

  1. . Altun Y., “Further results on the asymptotic stability of Riemann–Liouville fractional neutral systems with variable delays”, Adv. Difference Equ., 437, (2019), 1-13. [2]. Altun, Y. “Improved results on the stability analysis of linear neutral systems with delay decay approach”, Math Meth Appl Sci., 43, (2020), 1467–1483. [3]. Altun Y., “New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags”, BEU Journal of Science, 8, (2019), 443-450. [4]. Altun Y., Tunç C., “New Results on the Exponential Stability of Solutions of Periodic Nonlinear Neutral Differential Systems”, Dynamic Systems and Applications, 28, (2019), 303-316. [5]. Chartbupapan C., Bagdasar O., Mukdasai K., “A Novel Delay-Dependent Asymptotic Stability Conditions for Differential and Riemann-Liouville Fractional Differential Neutral Systems with Constant Delays and Nonlinear Perturbation”, Mathematics, 8, (2020), 1-10. [6]. Ding Y., Zhong S., Chen W., “A delay-range-dependent uniformly asymptotic stability criterion for a class of nonlinear singular systems”, Nonlinear Anal. Real World Appl., 12, (2011), 1152–1162. [7]. Duarte-Mermoud M.A., Aguila-Camacho N., Gallegos J.A., Castro-Linares R., “Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems” Commun. Nonlinear Sci. Numer. Simul., 22, (2015), 650–659. [8]. Feng Y., Zhu X., Zhang Q., “Delay-dependent stability criteria for singular time-delay systems”, Acta Automat. Sin., 36, (2010), 433–437. [9]. Feng Z., Lam J., Gao H., “α-dissipativity analysis of singular time-delay systems” Automatica, 47, (2011), 2548–2552. [10]. Fridman E., Shaked U., “H∞ control of linear state-delay descriptor systems: an LMI approach”, Linear Algebra Appl., 351, (2002), 271–302. [11]. Guabao L., “New results on stability analysis of singular time delay systems”, International Journal of Systems Science, 48, (2017), 1395–1403. [12]. Hale J., “Theory of Functional Differential Equations” in Springer-Verlag, New York, USA, 1977. [13]. Kilbas A.A., Srivastava H.M., Trujillo J.J., “Theory and Application of Fractional Differential Equations” in Elsevier, New York, USA, (2006). [14]. Liu S., Li X., Zhou X.F., Jiang W., “Lyapunov stability analysis of fractional nonlinear systems”, Appl. Math. Lett., 51, (2016), 13–19. [15]. Liu S., Wu X., Zhang Y.J., Yang R., “Asymptotical stability of Riemann–Liouville fractional neutral systems”, Appl. Math. Lett., 69,(2017), 168–173. [16]. Liu S