Asymptotic stability of neutral stochastic pantograph systems with Markovian switching

References

• Baker, C. T. H., & Buckwar, E. (2000). Continuous θ−methods for the stochastic pantograph equation. Electronic Transactions on Numerical Analysis, 11, 131–151. https://doi.org/10.1016/0377-0273(76)90010-X
   Google Scholar
• Caraballo, T., Mchiri, L., Mohsen, B., & Rhaima, M. (2021a). pth moment exponential stability of neutral stochastic pantograph differential equation with Markovian switching. Communications in Nonlinear Science and Numerical Simulation, 102, 105916. https://doi.org/10.1016/j.cnsns.2021.105916
   Web of Science ®Google Scholar
• Caraballo, T., Mohsen, B., Mchiri, L., & Rhaima, M. (2021b). h-stability in pth moment of neutral pantograph stochastic differential equations with Markovian switching driven by Lévy noise. Chaos, Solitons $\mathrm{\&}$ Fractals, 151, 111249. https://doi.org/10.1016/j.chaos.2021.111249
   Web of Science ®Google Scholar
• Deng, Y., Huang, C., & Cao, J. (2021). New results on dynamics of neutral type HCNNs with proportional delays. Mathematics and Computers in Simulation, 187, 51–59. https://doi.org/10.1016/j.matcom.2021.02.001
   Web of Science ®Google Scholar
• Guo, P., & Li, C. (2019). Razumikhin-type theorems on the moment stability of the exact and numerical solutions for the stochastic pantograph differential equations. Journal of Computational and Applied Mathematics, 355, 77–90. https://doi.org/10.1016/j.cam.2019.01.011
   Web of Science ®Google Scholar
• Guo, Y., Ding, X., & Li, Y. (2016). Stochastic stability for pantograph multi-group models with dispersal and stochastic perturbation. Journal of the Franklin Institute, 353(13), 2980–2998. https://doi.org/10.1016/j.jfranklin.2016.06.001
   Web of Science ®Google Scholar
• Hu, L., Mao, X., & Shen, Y. (2013). Stability and boundedness of nonlinear hybrid stochastic differential delay equations. Systems & Control Letters, 62(2), 178–187. https://doi.org/10.1016/j.sysconle.2012.11.009
   Web of Science ®Google Scholar
• Hua, M., Tan, H., Chen, J., & Fei, J. (2015). Robust delay-range-dependent non-fragile H∞ filtering for uncertain neutral stochastic systems with Markovian switching and mode-dependent time delays. Journal of The Franklin Institute, 352(3), 1318–1341. https://doi.org/10.1016/j.jfranklin.2014.12.020
   Web of Science ®Google Scholar
• Hua, M., Tan, H., Chen, J., & Ni, J. (2017). Robust stability and H∞ filter design for neutral stochastic neural networks with parameter uncertainties and time-varying delay. International Journal of Machine Learning and Cybernetics, 8(2), 511–524. https://doi.org/10.1007/s13042-015-0342-9
   Web of Science ®Google Scholar
• Li, J., & Ren, Y. (2022). Practical stability in relation to a part of variables of stochastic pantograph differential equations. International Journal of Control, 95(12), 3196–3201. https://doi.org/10.1080/00207179.2021.1961167.
   Web of Science ®Google Scholar
• Li, R., Liu, M., & Pang, W. (2009). Convergence of numerical solutions to stochastic pantograph equations with Markovian switching. Applied Mathematics and Computation, 215(1), 414–422. https://doi.org/10.1016/j.amc.2009.05.005
   Web of Science ®Google Scholar
• Li, X., & Mao, X. (2012). A note on almost sure asymptotic stability of neutral stochastic delay differential equations with Markovian switching. Automatica, 48(9), 2329–2334. https://doi.org/10.1016/j.automatica.2012.06.045
   Web of Science ®Google Scholar
• Li, X., Wang, N., Lou, J., & Lu, J. (2020). Global μ-synchronization of impulsive pantograph neural networks. Neural Networks, 131, 78–92. https://doi.org/10.1016/j.neunet.2020.07.004
   PubMed Web of Science ®Google Scholar
• Liu, L., & Deng, F. (2018). pth moment exponential stability of highly nonlinear neutral pantograph stochastic differential equations driven by Lévy noise. Applied Mathematics Letters, 86, 313–319. https://doi.org/10.1016/j.aml.2018.07.003
   Web of Science ®Google Scholar
• Mao, W., Hu, L., & Mao, X. (2019). Almost sure stability with general decay rate of neutral stochastic pantograph equations with Markovian switching. Electronic Journal of Qualitative Theory of Differential Equations, 52, 1–17. https://doi.org/10.14232/ejqtde.2019.1.52
   Google Scholar
• Mao, W., Hu, L., & Mao, X. (2020). The asymptotic stability of hybrid stochastic systems with pantograph delay and non-Gaussian Lévy noise. Journal of the Franklin Institute, 357(2), 1174–1198. https://doi.org/10.1016/j.jfranklin.2019.11.068
   Web of Science ®Google Scholar
• Mao, X. (1999). LaSalle-type theorems for stochastic differential delay equations. Journal of Mathematical Analysis and Applications, 236(2), 350–369. https://doi.org/10.1006/jmaa.1999.6435
   Web of Science ®Google Scholar
• Mao, X. (2007). Stochastic differential equations and applications. (2nd ed.). Horwood Publishing Limited.
   Google Scholar
• Mao, X., Shen, Y., & Yuan, C. (2008). Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching. Stochastic Processes and Their Applications, 118(8), 1385–1406. https://doi.org/10.1016/j.spa.2007.09.005
   Web of Science ®Google Scholar
• Mao, X., & Yuan, C. (2006). Stochastic differential equations with Markovian switching. Imperial College Press.
   Google Scholar
• Milošević, M. (2014). Existence, uniqueness, almost sure polynomial stability of solution to a class of highly nonlinear pantograph stochastic differential equations and the Euler–Maruyama approximation. Applied Mathematics and Computation, 237, 672–685. https://doi.org/10.1016/j.amc.2014.03.132
   Web of Science ®Google Scholar
• Ockendon, J. R., & Tayler, A. B. (1971). The dynamics of a current collection system for an electric locomotive. Proceedings of the Royal Society of London, 322, 447–468. https://doi.org/10.1098/rspa.1971.0078
   Google Scholar
• Shen, M., Fei, W., Mao, X., & Deng, S. (2020). Exponential stability of highly nonlinear neutral pantograph stochastic differential equations. Asian Journal of Control, 22(1), 436–448. https://doi.org/10.1002/asjc.v22.1
   Web of Science ®Google Scholar
• Song, R., Wang, B., & Zhu, Q. (2021). Delay-dependent stability of nonlinear hybrid neutral stochastic differential equations with multiple delays. International Journal of Robust and Nonlinear Control, 31(1), 250–267. https://doi.org/10.1002/rnc.v31.1
   Web of Science ®Google Scholar
• Song, Y., Zeng, Z., & Zhang, T. (2021). The pth moment asymptotical ultimate boundedness of pantograph stochastic differential equations with time-varying coefficients. Applied Mathematics Letters, 121, 107449. https://doi.org/10.1016/j.aml.2021.107449
   Web of Science ®Google Scholar
• Wang, T., & Zhu, Q. (2019). Stability analysis of stochastic BAM neural networks with reaction–diffusion, multi-proportional and distributed delays. Physica A: Statistical Mechanics and Its Applications, 533, Article ID 121935. https://doi.org/10.1016/j.physa.2019.121935
   Web of Science ®Google Scholar
• Wu, F., & Hu, S. (2012). The LaSalle-type theorem for neutral stochastic functional differential equations with infinite delay. Discrete and Continuous Dynamical Systems, 32(3), 1065–1094. https://doi.org/10.3934/dcds.2012.32.1065
   Web of Science ®Google Scholar
• Xiao, Q., Huang, T., & Zeng, Z. (2022). Synchronization of timescale-type nonautonomous neural networks with proportional delays. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 52(4), 2167–2173. https://doi.org/10.1109/TSMC.2021.3049363
   Web of Science ®Google Scholar
• Xu, L., & Hu, H. (2021). Boundedness analysis of stochastic pantograph differential systems. Applied Mathematics Letters, 111, Article ID 106630. https://doi.org/10.1016/j.aml.2020.106630
   Web of Science ®Google Scholar
• You, S., Mao, W., Mao, X., & Hu, L. (2015). Analysis on exponential stability of hybrid pantograph stochastic differential equations with highly nonlinear coefficients systems. Applied Mathematics and Computation, 263, 73–83. https://doi.org/10.1016/j.amc.2015.04.022
   Web of Science ®Google Scholar
• Yu, Y. (2016). Global exponential convergence for a class of HCNNs with neutral time-proportional delays. Applied Mathematics and Computation, 285, 1–7. https://doi.org/10.1016/j.amc.2016.03.018
   Web of Science ®Google Scholar
• Zhang, W., Gao, Y., Guo, Q., & Yao, X. (2019). The partially truncated Euler–Maruyama method for nonlinear pantograph stochastic differential equations. Applied Mathematics and Computation, 346, 109–126. https://doi.org/10.1016/j.amc.2018.10.052
   Web of Science ®Google Scholar
• Zhao, D., Wang, Z., Wei, G., & Liu, X. (2021). Nonfragile H∞ state estimation for recurrent neural networks with time-Varying delays: on proportional-integral observer design. IEEE Transactions on Neural Networks and Learning Systems, 32(8), 3553–3565. https://doi.org/10.1109/TNNLS.2020.3015376
   PubMed Web of Science ®Google Scholar
• Zhao, Y., & Zhu, Q. (2021). Stabilization by delay feedback control for highly nonlinear switched stochastic systems with time delays. International Journal of Robust and Nonlinear Control, 31(8), 3070–3089. https://doi.org/10.1002/rnc.v31.8
   Web of Science ®Google Scholar
• Zhou, S., & Xue, M. (2014). Exponential stability for nonlinear hybrid stochastic pantograph equations and numerical approximation. Acta Mathematica Scientia, 34(4), 1254–1270. https://doi.org/10.1016/S0252-9602(14)60083-7
   Web of Science ®Google Scholar
• Zhou, W., Zhou, X., Yang, J., Zhou, J., & Tong, D. (2018). Stability analysis and application for delayed neural networks driven by fractional Brownian noise. IEEE Transactions on Neural Networks and Learning Systems, 29(5), 1491–1502. https://doi.org/10.1109/TNNLS.2017.2674692
   PubMed Web of Science ®Google Scholar
• Zhou, X., Yang, J., Li, Z., Zhou, W., & Tong, D. (2017). Stability analysis based on partition trajectory approach for switched neural networks with fractional Brown noise disturbance. International Journal of Control, 90(10), 2165–2177. https://doi.org/10.1080/00207179.2016.1237047
   Web of Science ®Google Scholar
• Zhou, X., Zhou, W., Dai, A., Yang, J., & Xie, L. (2015). Asymptotical stability of stochastic neural networks with multiple time-varying delays. International Journal of Control, 88(3), 613–621. https://doi.org/10.1080/00207179.2014.971343
   Web of Science ®Google Scholar