Stabilization by delay feedback control for highly nonlinear HSDDEs driven by Lévy noise

[1] D. Applebaum, L´evy Processes and Stochastic Calculus, 2nd Edition, Cambridge University Press,
2009.
[2] D. Applebaum, M. Siakalli, Stochastic stabilization of dynamical systems using L´evy noise, Stoch.
Dyn. 10 (2010) 509–527.
[3] A. Bahar, X. Mao, Stochastic delay population dynamics, Int. J. Pure Appl. Math. 11 (2004) 377–
400.
[4] M. Fatehi Nia, E. Mirzavand, Stochastic dynamics of Izhikevich-Fitzhugh neuron model, J. Math.
Model. 12 (2024) 199–214.
[5] C. Fei, W. Fei, X. Mao, M. Shen, L. Yan, Stability analysis of highly nonlinear hybrid multiple-
delay stochastic differential equations, J. Appl. Anal. Comput. 9 (2019) 1053–1070.
[6] D. He, L. Xu, Boundedness analysis of stochastic delay differential equations with L´evy noise,
Appl. Math. Comput. 421 (2022) 126902.
[7] L. Hu, X. Mao, Y. Shen, Stability and boundedness of nonlinear hybrid stochastic differential delay
equations, Syst. Control Lett. 62 (2013) 178–187.

[8] L. Huang, X. Mao, Delay-dependent exponential stability of neutral stochastic delay systems, IEEE
Trans. Autom. Control. 54 (2009) 147–152.
[9] M. Loeve, Probability theory, D. Van Nostrand Company, Inc, 1955.
[10] G. Li, Stabilization of stochastic regime-switching Poisson jump equations by delay feedback con-
trol, J. Inequal. Appl. 1 (2022) 20.
[11] M. Li, F. Deng, Almost sure stability with general decay rate of neutral stochastic delayed hybrid
systems with L´evy noise, Nonlinear Anal. Hybrid Syst. 24 (2017) 171–185.
[12] G. Li, Z. Hu, F. Deng, H. Zhang, Stabilization via delay feedback for highly nonlinear stochastic
time-varying delay systems with Markovian switching and Poisson jump, Electron. J. Qual. Theory
Differ. Equ. 49 (2022) 1–20.
[13] W. Li, C. Fei, C. Mei, W. Fei, X. Mao, Delay tolerance for stable hybrid stochastic differential
equations with L´evy noise based on Razumikhin technique, Syst. Control Lett. 176 (2023) 105530.
[14] X. Li, X. Mao, Stabilisation of highly nonlinear hybrid stochastic differential delay equations by
delay feedback control, Automatica 112 (2020) 108657.
[15] G. Li, Q. Yang, Stability analysis between the hybrid stochastic delay differential equations with
jumps and the Euler-Maruyama method, J. Appl. Anal. Comput. 11 (2021) 1259–1272.
[16] G. Li, Q. Yang, Stabilization of hybrid stochastic systems with L´evy noise by discrete-time feedback
control, Int. J. Control. 95 (2020) 197–205.
[17] D. Liu, W. Wang, J. Menaldi, Almost sure asymptotic stabilization of differential equations with
time-varying delay by L´evy noise, Nonlinear Dyn. 79 (2015) 163–172.
[18] M. Liu, Y. Zhu, Stationary distribution and ergodicity of a stochastic hybrid competition model
with L´evy jumps, Nonlinear Anal. Hybrid Syst. 30 (2018) 225–239.
[19] Z. Lu, J. Hu, X. Mao, Stabilisation by delay feedback control for highly nonlinear hybrid stochastic
differential equations, Discrete Contin. Dyn. Syst. Ser. B. 24 (2019) 4099–4116.
[20] X. Mao, Stability of stochastic differential equations with Markovian switching, Stoch. Proc. Appl.
79 (1999) 45–67.
[21] W. Mao, L. Hu, X. Mao, The asymptotic stability of hybrid stochastic systems with pantograph
delay and non-Gaussian L´evy noise, J. Franklin Inst. 357 (2020) 1174–1198.
[22] X. Mao, A. Matasov, A. Piunovskiy, Stochastic differential delay equations with Markovian switch-
ing, Bernoulli. 6 (2000) 73–90.
[23] X. Mao, L. Shaikhet, Delay-dependent stability criteria for stochastic differential delay equations
with Markovian switching, Stab. Control Theory Appl. 3 (2000) 88–102.
[24] X. Mao, C. Yuan, Stochastic Differential Equations with Markovian Switching, Imperial College
Press, London, 2006.

[25] M. Rhaima, L. Mchiri, A. Makhlouf, H∞ and Asymptotic Stability via delay feedback for hybrid
neutral stochastic delay differential equations with L´evy noise, IMA J. Math. Control Inform. 40
(2023) 106–132.
[26] T. Tian, K. Burrage, P. Burrage, M. Carletti, Stochastic delay differential equations for genetic
regulatory networks, J. Comput. Appl. Math. 205 (2007) 696–707.
[27] F. Wan, P. Hu, H. Chen, Stability analysis of neutral stochastic dfferential delay equations driven
by L´evy noises, Appl. Math. Comput. 375 (2020) 125080.
[28] L. Wu, X. Su, P. Shi, Sliding mode control with bounded L2 gain performance of Markovian jump
singular time-delay systems, Automatica. 48 (2012) 1929–1933.
[29] A. Wu, H. Yu, Z. Zeng, Variable-delay feedback control for stabilisation of highly nonlinear hybrid
stochastic neural networks with time-varying delays, Int. J. Control. 97 (2023) 744–755.
[30] C. Yuan, X. Mao, Stability of stochastic delay hybrid systems with jumps, Eur. J. Control. 6 (2010)
595–608.
[31] Q. Zhu, Asymptotic stability in the pth moment for stochastic differential equations with L´evy noise,
J. Math. Anal. Appl. 416 (2014) 126-142.