References
- Khasminskii RZ. A limit theorem for the solution of differential equations with random right-hand sides. Theory Probab Appl. 1963;11:390–405.
- Roberts JB, Spanos PD. Stochastic averaging: an approximate method of solving random vibration problems. Int J Nonlinear Mech. 1986;21(2):111–134.
- Zhu WQ. Stochastic averaging methods in random vibration. Appl Mech Rev. 1988;41(5):189–199.
- Xu Y, Duan J, Xu W. An averaging for stochastic dynamical systems with Lévy noise. Physica D. 2011;240:1395–1401.
- Xu Y, Guo R, et al. Stochastic averaging for dynamical systems with fractional Brownian motion. Discr Cont Dyn B. 2014;19:1197–1212.
- Xu Y, Pei B, Guo R. Stochastic averaging for slow–fast dynamical systems with fractional Brownian motion. Discr Cont Dyn B. 2015;20:2257–2267.
- Xu Y, Pei B, Wu JL. Stochastic averaging principle for differential equations with non-Lipschitz coefficients driven by fractional Brownian motion. Discr Cont Dyn B. 2017;17(2):1750013.
- Maslowski B, Seidler J, Vrkoč I. An averaging principle for stochastic evolution equations II. Math Bohemica. 1991;116(2):191–224.
- Bao JH, Yin G, Yuan CG. Two-time-scale stochastic partial differential equations driven by α-stable noises: averaging principles. Bernoulli. 2017;23(1):645–669.
- Pei B, Xu Y, Yin G. Stochastic averaging for a class of two-time-scale systems of stochastic partial differential equations. Nonlinear Anal. 2017;160:159–176.
- Pei B, Xu Y, Yin G, et al. Averaging principles for functional stochastic partial differential equations driven by a fractional Brownian motion modulated by two-time-scale Markovian switching processes. Nonlinear Anal-Hybri. 2018;27:107–124.
- Zhu QX. Stabilization of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. IEEE Trans Automat Contr. 2021;64(9):3764–3771.
- Ding K, Zhu QX. Extended dissipative anti-disturbance control for delayed switched singular semi-Markovian jump systems with multi-disturbance via disturbance observer. Automatica. 2021;128:109556.
- Tan L, Ding YL. The averaging method for stochastic differential delay equations under non-Lipschitz conditions. Adv. Differ. Equ-NY. 2013;2013:38.
- Xu Y, Pei B, Yang YG. An averaging principle for stochastic differential delay equations with fractional Brownian motion. Abstr Appl Anal. 2014;2014:479195.
- Mao W, You SR, Wu XQ, et al. On the averaging principle for stochastic delay differential equations with jumps. Adv Differ Equ NY. 2015;2015(1):70.
- Mao W, Mao XR. An averaging principle for neutral stochastic functional differential equations driven by Poisson random measure. Adv Differ Equ NY. 2016(1):77.
- He XY, Han S, Tao J. Averaging principle for SDEs of neutral type driven by G-Brownian motion. Stoch Dyn. 2019(1):1950004.
- Lakshmikantham V, Bainov DD, Simeonov PS. Theory of impulsive differential equations. Singapore: World Scientific; 1989.
- Liu JK, Xu W, Guo Q. Global attractiveness and exponential stability for impulsive fractional neutral stochastic evolution equations driven by fBm. Adv Differ Equ. 2020;63:1–17.
- Hu W, Zhu QX. Stability criteria for impulsive stochastic functional differential systems with distributed-delay dependent impulsive effects. IEEE Trans Syst Man Cybern Syst. 2021;51(3):2027–2032.
- Hu W, Zhu QX, Karimi HR. Some improved Razumikhin stability criteria for impulsive stochastic delay differential systems. IEEE Trans Automat Contr. 2021;64(12):5207–5213.
- Perestyuk N, et al. Differential equations with impulse effects: multivalued right-hand sides with discontinuities. Berlin: Walter de Gruyter; 2011.
- Mesquita JG, Slavík A. Periodic averaging theorems for various types of equations. J Math Anal Appl. 2012;387(2):862–877.
- Federson M, Mesquita JG, Slavík A. Basic results for functional differential and dynamic equations involving impulses. Math Nachr. 2013;286:181–204.
- Ma S, Kang YM. Periodic averaging method for impulsive stochastic differential equations with Lévy noise. Appl Math Lett. 2019;93:91–97.
- Liu JK, Xu W, et al. Periodic averaging theorems for neutral stochastic functional differential equations involving delayed impulses. Stochastics. 2020. DOI: 10.1080/17442508.2020.1817023.
- Liu JK, Xu W. An averaging result for impulsive fractional neutral stochastic differential equations. Appl Math Lett. 2021;114:106892.
- Mitropolskii YA, Rogovchenko YV. Averaging of impulse evolution systems. Ukr Math J. 1992;44(1):68–74.
- Liu JK, Xu W, Guo Q. Averaging principle for impulsive stochastic partial differential equations. Stoch Dyn. 2021;2150014. DOI:10.1142/S0219493721500143.
- Cheng P, Deng FQ, Yao FQ. Exponential stability analysis of impulsive stochastic functional differential systems with delayed impulses. Commun Nonlinear Sci. 2014;19(6):2104–2114.
- Pazy A. Semigroups of linear operators and applications to partial differential equations. New York: Springer Science & Business Media; 2012.
- Da Prato G, Zabczyk J. Stochastic equations in infinite dimensions. Cambridge: Cambridge University Press; 2014.
- Sakthivel R. Approximate controllability of impulsive stochastic evolution equations. Funkc Ekvacioj-Ser I. 2009;52(3):381–393.
- Vrkoč I. Weak averaging of stochastic evolution equations. Math Bohem. 1995;120(1):91–111.