Finite-time stability of linear stochastic fractional-order systems with time delay

Lassaad Mchiri1, Abdellatif Ben Makhlouf2, Dumitru Băleanu3, Mohamed Rhaima1
1Department of Statistics and Operations Research, College of Sciences, King Saud University, P. O Box 2455, Riyadh, 11451, Saudi Arabia
2Mathematics Department, College of Science, Jouf University, P.O. Box: 2014, Sakaka, Saudi Arabia
3Department of Mathematics, Cankaya University, Ankara, Turkey

Tóm tắt

Abstract

This paper focuses on the finite-time stability of linear stochastic fractional-order systems with time delay for $\alpha \in (\frac{1}{2},1)$ α ( 1 2 , 1 ) . Under the generalized Gronwall inequality and stochastic analysis techniques, the finite-time stability of the solution for linear stochastic fractional-order systems with time delay is investigated. We give two illustrative examples to show the interest of the main results.

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Tài liệu tham khảo

Adiguzel, R.S., Aksoy, U., Karapinar, E., Erhan, I.M.: On the solution of a boundary value problem associated with a fractional differential equation. Math. Methods Appl. Sci. (2020). https://doi.org/10.1002/mma.6652

Afshari, H., Kalantari, S., Karapinar, E.: Solution of fractional differential equations via coupled fixed point. Electron. J. Differ. Equ. 2015, 1 (2015)

Alqahtani, B., Aydi, H., Karapinar, E., Rakocevic, V.: A solution for Volterra fractional integral equations by hybrid contractions. Mathematics 7(8), 694 (2019). https://doi.org/10.3390/math7080694

Amato, F., Ambrosino, R., Cosentino, C., Tommasi, G.D.: Finite-time stabilization of impulsive dynamical linear systems. Nonlinear Anal. Hybrid Syst. 5, 89–101 (2011)

Ben Makhlouf, A., Nagy, A.M.: Finite-time stability of linear Caputo–Katugampola fractional-order time delay systems. Asian J. Control 22, 297–306 (2020)

Caraballo, T., Hammami, M., Mchiri, L.: Practical exponential stability of impulsive stochastic functional differential equations. Syst. Control Lett. 109, 43–48 (2017)

Feng, T., Wu, B.W., Liu, L., Wang, Y.E.: Finite-time stability and stabilization of fractional-order switched singular continuous-time systems. Circuits Syst. Signal Process. 38, 5528–5548 (2019)

Hussaina, S., Sadiaa, H., Aslama, S.: Some generalized Gronwall–Bellman–Bihari type integral inequalities with application to fractional stochastic differential equation. Filomat 33(3), 815–824 (2019)

Jmal, A., Ben Makhlouf, A., Nagy, A.M., Naifar, O.: Finite-time stability for Caputo-Katugampola fractional-order time-delayed neural networks. Neural Process. Lett. 50, 607–621 (2019). https://doi.org/10.1007/s11063-019-10060-6

Jmal, A., Naifar, O., Ben Makhlouf, A., Derbel, N., Hammami, M.A.: On observer design for nonlinear Caputo fractional order systems. Asian J. Control 20, 1533–1540 (2017)

Jmal, A., Naifar, O., Ben Makhlouf, A., Derbel, N., Hammami, M.A.: Sensor fault estimation for fractional-order descriptor one-sided Lipschitz systems. Nonlinear Dyn. 31, 1713–1722 (2017)

Jmal, A., Naifar, O., Ben Makhlouf, A., Derbel, N., Hammami, M.A.: Robust sensor fault estimation for fractional-order systems with monotone nonlinearities. Nonlinear Dyn. 90, 2673–2685 (2017)

Liang, J., Wu, B.W., Wang, Y.E., Niu, B., Xie, X.: Input-output finite-time stability of fractional-order positive switched systems. Circuits Syst. Signal Process. 38, 1619–1638 (2019)

Mao, X.: Stochastic Differential Equations and Applications. Ellis Horwood, Chichester (1997)

Mathiyalaganm, K., Balachandran, K.: Finite-time stability of fractional-order stochastic singular systems with time delay and white noise. Complexity 21, 370–379 (2019)

Moulay, E., Dambrine, M., Yeganefar, N., Perruquetti, W.: Finite-time stability and stabilization of time-delay systems. Syst. Control Lett. 57, 561–566 (2008)

Naifar, O., Ben Makhlouf, A., Hammami, M.A.: Comments on “Lyapunov stability theorem about fractional system without and with delay”. Commun. Nonlinear Sci. Numer. Simul. 30, 360–361 (2016)

Naifar, O., Ben Makhlouf, A., Hammami, M.A.: Comments on “Mittag-Leffler stability of fractional order nonlinear dynamic systems”. Automatica 75, 329 (2017)

Naifar, O., Ben Makhlouf, A., Hammami, M.A., Chen, L.: Global practical Mittag leffer stabilization by output feedback for a class of nonlinear fractional order systems. Asian J. Control 20, 599–607 (2017)

Naifar, O., Nagy, A.M., Ben Makhlouf, A., Kharrat, M., Hammami, M.A.: Finite time stability of linear fractional order time delay systems. Int. J. Robust Nonlinear Control 29, 180–187 (2019)

Wang, F., Chen, D., Zhang, X., Wu, Y.: Finite-time stability of a class of nonlinear fractional-order system with the discrete time delay. Int. J. Syst. Sci. 48, 984–993 (2017)

Wang, G., Liu, L., Zhang, Q., Yang, C.: Finite-time stability and stabilization of stochastic delayed jump systems via general controllers. J. Franklin Inst. 354, 938–966 (2014)

Xu, J., Sun, J.: Finite-time stability of nonlinear switched impulsive systems. Int. J. Syst. Sci. 44, 889–895 (2013)