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

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

Kaynakça

[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., Wu X., Zhou X.F., Jiang W., “Asymptotical stability of Riemann-Liouville fractional nonlinear systems”, Nonlinear Dynamics, 86, (2016), 65–71.

[17]. Liu S., Zhou X.F., Li X., Jiang W., “Stability of fractional nonlinear singular systems its applications in synchronization of complex dynamical networks” Nonlinear Dynam., 84, (2016), 2377–2385.

[18]. Liu S., Zhou X.F., Li X., Jiang W., “Asymptotical stability of Riemann–Liouville fractional singular systems with multiple time-varying delays”, Appl. Math. Lett., 65, (2017), 32–39.

[19]. Liu Z.Y., Lin C., Chen B., “A neutral system approach to stability of singular time-delay systems”, J. Franklin Inst., 351, (2014), 4939–4948.

[20]. Lu Y.F., Wu R.C., Qin Z.Q., “Asymptotic stability of nonlinear fractional neutral singular systems”, J. Appl. Math. Comput., 45, (2014), 351–364.

[21]. Podlubny I., “Fractional Differential Equations” in Academic Press., New York, USA, 1999.

[22]. Qian D., Li C., Agarwal R.P., Wong P.J.Y., “Stability analysis of fractional differential system with Riemann–Liouville derivative”, Math. Comput. Model., 52, (2010), 862–874.

[23]. Sabatier J., Moze M., Farges C., “LMI stability conditions for fractional order systems” Comput. Math. Appl., 59, (2010), 1594-1609.

[24]. Tunç C., Altun Y., “Asymptotic stability in neutral differential equations with multiple delays”, J. Math. Anal., 7, (2016), 40–53.

[25]. Xu S., Van Dooren P., Stefan R., “Robust stability and stabilization for singular systems with state delay and parameter uncertainty”, IEEE Trans. Autom. Control, 47, (2002), 1122–1128.

[26]. Yiğit A., Tunç C. “On the stability and admissibility of a singular differential system with constant delay”, International Journal of Mathematics and Computer Science, 15, (2020), 641–660.

[27]. Zhou X. F., Hu L.G., Liu S., Jiang W., “Stability criterion for a class of nonlinear fractional differential systems”, Appl. Math. Lett., 28, (2014), 25–29.

Kaynak Göster

  • ISSN: 1694-7398
  • Yayın Aralığı: Yılda 2 Sayı
  • Başlangıç: 2001

330 69

Sayıdaki Diğer Makaleler

Detection of some antioxidant enzyme activities in apricot fruit grown in Van region from Turkey

Mustafa BİLİCİ

Analysis of Turkish 6/49 lottery results

Alper VAHAPLAR, Murat Erşen BERBERLER

Fault analysis and prediction of power distribution networks on 11kV Feeders: A case study of Eleweeran and Poly Road 11kV Feeders, Abeokuta

Omowumi G. OLASUNKANMI, Ajibola O. OYEDEJI, Ayodeji A. OKUBANJO

Real time traffic signal timing approach based on artificial neural network

Ali Tahir KARAŞAHİN, Abdullah Erdal TÜMER

Stability of the third order rational difference equation

Mehmet Emre ERDOGAN

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

Yener ALTUN

Ferrocene as a leaving group; Unexpected rearrangement reactions for the synthesis of 2,3-diarylnapthoquinones

Nevroz Aslan ERTAS, Arif KIVRAK

Modelling occupational health and safety risks among unskilled workers in construction industry

Hezekiah Oluwole ADEYEMI, Olatilewa Rapheal ABOLADE, Ajibola Oluwafemi OYEDEJI, Olanrewaju Bilikis OLATUNDE

The concentration distribution of components and particles in the system: tomato-water-sodium nitrate and assessment of the oxidation-reduction potential at different temperatures

Damira SAMBAEVA, Timur MAİMEKOV, Nurzat SHAYKİEVA, Janarbek IZAKO, Zarlyk MAİMEKOV

Carbon nanotube supported direct borohydride fuel cell anode catalysts: the effect of catalyst loading

Hilal Demir KIVRAK, Aykut ÇAĞLAR, Tulin Avcı HANSU, Ömer ŞAHİN