Exponential input-to-state stability for neutral stochastic delay differential equations with Lévy noise and Markovian switching

References

• A. Bellen, Z. Jackiewicz, and M. Zennaro, Numerical stability of nonlinear delay differential equations of neutral type, J. Comput. Appl. Math. 125 (2000), pp. 251–263.
   Web of Science ®Google Scholar
• W. Cao and Q. Zhu, Stability analysis of neutral stochastic delay differential equations via the vector Lyapunov function method, Appl. Math. Comput. 405 (2021), p. 126257.
   Google Scholar
• T. Caraballoa, M. Belfeki, L. Mchiri, and M. Rhaima, h-stability in pth moment of neutral pantograph stochastic differential equations with Markovian switching driven by Lévy noise, Chaos Solitons Fract. 151 (2021), pp. 111249.
   Google Scholar
• I. Chafa, Stability for Markovian switching stochastic neural networks with infinite delay driven by Lévy noise, Int. J. Dyn. Control 7 (2019), pp. 547–556.
   Google Scholar
• W. Chen, S. Xu, and Y. Zou, Stabilization of hybrid neutral stochastic differential delay equations by delay feedback control, Syst. Control Lett. 88 (2016), pp. 1–13.
   Web of Science ®Google Scholar
• H. Chen, P. Shi, and C.C. Lim, Stability analysis for neutral stochastic delay systems with Markovian switching, Syst. Control Lett. 110 (2017), pp. 38–48.
   Web of Science ®Google Scholar
• F. Deng, W. Mao, and A. Wan, A novel result on stability analysis for uncertain neutral stochastic time-varying delay systems, Appl. Math. Comput. 221 (2013), pp. 132–143.
   Web of Science ®Google Scholar
• Y. Fan and H. Chen, Input-to-state stability for stochastic delay neural networks with Markovian Switching, Neural Process. Lett. 53 (2021), pp. 4389–4406.
   Web of Science ®Google Scholar
• L. Huang and X. Mao, On input-to-state stability of stochastic retarded systems with Markovian Switching, IEEE Trans. Autom. Control 54 (2009), pp. 1898–1902.
   Web of Science ®Google Scholar
• H. Ito, Input-to-state stability and Lyapunov functions with explicit domains for SIR model of infectious diseases, Discret. Contin. Dyn. Syst. Ser. B 26 (2021), pp. 5171–5196.
   Web of Science ®Google Scholar
• V. Kolmanovskii, N. Koroleva, T. Maizenberg, X. Mao, and A. Matasov, Neutral stochastic differential delay equations with Markovian switching, Stoch. Anal. Appl. 21 (2003), pp. 819–847.
   Web of Science ®Google Scholar
• S. Kuang, F. Deng, and Y. Peng, Input-to-state stability of Euler–Maruyama method for stochastic delay control systems, J. Syst. Eng. Electron. 24 (2013), pp. 309–317.
   Web of Science ®Google Scholar
• G. Ladas and Y.G. Sficas, Oscillations of neutral delay differential equations, Can. Math. Bul.-Bul. Can. Math. 29 (1986), pp. 438–445.
   Web of Science ®Google Scholar
• M. Li and F. Deng, Almost sure stability with general decay rate of neutral stochastic delayed hybrid systems with Lévy noise, Nonlinear Anal. Hybrid Syst. 24 (2017), pp. 171–185.
   Web of Science ®Google Scholar
• M. Li and F. Deng, Moment exponential input-to-state stability of non-linear switched stochastic systems with Lévy noise, IET-Control Theory Appl. 12 (2018), pp. 1208–1215.
   Web of Science ®Google Scholar
• C. Li and J. Luo, Stochastic invariance for neutral functional differential equation with non-Lipschitz coefficients, Discret. Contin. Dyn. Syst. Ser. B 24 (2019), pp. 3299–3318.
   Web of Science ®Google Scholar
• H. Li and J. Wang, Input-to-state stability of continuous-time systems via finite-time Lyapunov functions, Discret. Contin. Dyn. Syst. Ser. B 25 (2020), pp. 841–857.
   Web of Science ®Google Scholar
• H. Li, B. Chen, Q. Zhou, and S. Fang, Robust exponential stability for uncertain stochastic neural networks with discrete and distributed time-varying delays, Phys. Lett. A 372 (2008), pp. 3385–3394.
   Web of Science ®Google Scholar
• M. Li, L. Liu, and F. Deng, Input-to-state stability of switched stochastic delayed systems with Lévy noise, J. Frankl. Inst.-Eng. Appl. Math. 355 (2018), pp. 314–331.
   Web of Science ®Google Scholar
• J. Liu, Z. Li, and F. Deng, Asymptotic behavior analysis of Markovian switching neutral-type stochastic time-delay systems, Appl. Math. Comput. 404 (2021), pp. 126205.
   Google Scholar
• X. Mao and C. Yuan, Stochastic Differential Equations with Markovian Swithcing, Imperial College Press, London, 2006.
   Google Scholar
• X. Mao, Y. Shen, and C. Yuan, Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching, Stoch. Process. Appl. 118 (2008), pp. 1385–1406.
   Web of Science ®Google Scholar
• Y. Ou, H. Liu, Y. Si, and Z. Feng, Stability analysis of discrete-time stochastic neural networks with time-varying delays, Neurocomput. 73 (2010), pp. 740–748.
   Web of Science ®Google Scholar
• H. Peics and J. Karsai, Positive solutions of neutral delay differential equation, Novi. Sad. J. Math.32 (2002), pp. 95–108.
   Google Scholar
• M. Shen, W. Fei, X. Mao, and Y. Liang, Stability of highly nonlinear neutral stochastic differential delay equations, Syst. Control Lett. 115 (2018), pp. 1–8.
   Web of Science ®Google Scholar
• M. Shen, C. Fei, W. Fei, and X. Mao, Boundedness and stability of highly nonlinear hybrid neutral stochastic systems with multiple delays, Sci. China Inf. Sci. 62 (2019), pp. 1–16.
   PubMedGoogle Scholar
• Y. Song, W. Sun, and F. Jiang, Mean-square exponential input-to-state stability for neutral stochastic neural networks with mixed delays, Neurocomput. 205 (2016), pp. 195–203.
   Web of Science ®Google Scholar
• Q. Song, Z. Zhao, Y. Liu, and F.E. Alsaadi, Mean-square input-to-state stability for stochastic complex-valued neural networks with neutral delay, Neurocomput. 470 (2022), pp. 269–277.
   Web of Science ®Google Scholar
• E.D. Sontag, Smooth stabilization implies coprime factorization, IEEE Trans. Autom. Control 34 (1989), pp. 435–443.
   Web of Science ®Google Scholar
• Y. Sun, Y. Zhang, W. Zhou, J. Zhou, and X. Zhang, Adaptive exponential stabilization of neutral-type neural network with Lévy noise and Markovian switching parameters, Neurocomput. 284 (2018), pp. 160–170.
   Web of Science ®Google Scholar
• F. Wan, P. Hu, and H. Chen, Stability analysis of neutral stochastic differential delay equations driven by Lévy noises, Appl. Math. Comput. 375 (2020), pp. 125080.
   Google Scholar
• P. Wang, M. Zhang, and H. Su, Input-to-state stability of infinite-dimensional stochastic nonlinear systems, Discret. Contin. Dyn. Syst. Ser. B 27 (2022), pp. 821–836.
   Web of Science ®Google Scholar
• X. Wu, P. Shi, Y. Tang, and W. Zhang, Input-to-state stability of nonlinear stochastic time-varying systems with impulsive effects, Int. J. Robust Nonlin. 27 (2017), pp. 1792–1809.
   Web of Science ®Google Scholar
• A. Wu, S. You, W. Mao, X. Mao, and L. Hu, On exponential stability of hybrid neutral stochastic differential delay equations with different structures, Nonlinear Anal. Hybrid Syst. 39 (2021), p. 100971.
   Google Scholar
• L. Xu and D. Xu, Mean square exponential stability of impulsive control stochastic systems with time-varying delay, Phys. Lett. A 373 (2009), pp. 328–333.
   Web of Science ®Google Scholar
• D. Xu, B. Li, S. Long, and L. Teng, Moment estimate and existence for solutions of stochastic functional differential equations, Nonlinear Anal.: Theory Methods Appl. 108 (2014), pp. 128–143.
   Web of Science ®Google Scholar
• Y. Xu, W. Luo, K. Zhong, and S. Zhu, Mean square input-to-state stability of a general class of stochastic recurrent neural networks with Markovian switching, Neural Comput. Appl. 25 (2014), pp. 1657–1663.
   Web of Science ®Google Scholar
• W. Zhang, W. Zheng, and B. Chen, Detectability, observability and Lyapunov-type theorems of linear discrete time-varying stochastic systems with multiplicative noise, Int. J. Control 90 (2017), pp. 2490–2507.
   Web of Science ®Google Scholar
• B. Zhou, On asymptotic stability of linear time-varying systems, Automatica 68 (2016), pp. 266–276.
   Web of Science ®Google Scholar
• B. Zhou and W. Luo, Improved Razumikhin and Krasovskii stability criteria for time-varying stochastic time-delay systems, Automatica 89 (2018), pp. 382–391.
   Web of Science ®Google Scholar
• L. Zhou and X. Liu, Mean-square exponential input-to-state stability of stochastic recurrent neural networks with multi-proportional delays, Neurocomput. 219 (2017), pp. 396–403.
   Web of Science ®Google Scholar
• B. Zhou, G. Cai, and G. Duan, Stabilisation of time-varying linear systems via Lyapunov differential equations, Int. J. Control 86 (2013), pp. 332–347.
   Web of Science ®Google Scholar
• W. Zhou, L. Teng, and D. Xu, Mean-square exponentially input-to-state stability of stochastic Cohen–Grossberg neural networks with time-varying delays, Neurocomput. 153 (2015), pp. 54–61.
   Web of Science ®Google Scholar
• Q. Zhu, Asymptotic stability in the pth moment for stochastic differential equations with Lévy noise, J. Math. Anal. Appl. 416 (2014), pp. 126–142.
   Web of Science ®Google Scholar
• Q. Zhu, Razumikhin-type theorem for stochastic functional differential equations with Lévy noise and Markov switching, Int. J. Control 90(8) (2017), pp. 1703–1712.
   Web of Science ®Google Scholar
• Q. Zhu, Stability analysis of stochastic delay differential equations with Lévy noise, Syst. Control Lett. 118 (2018), pp. 62–68.
   Web of Science ®Google Scholar
• Q. Zhu and J. Cao, Mean-square exponential input-to-state stability of stochastic delayed neural networks, Neurocomput. 131 (2014), pp. 157–163.
   Web of Science ®Google Scholar
• Q. Zhu, J. Cao, and R. Rakkiyappan, Exponential input-to-state stability of stochastic Cohen–Grossberg neural networks with mixed delays, Nonlin. Dynam. 79 (2015), pp. 1085–1098.
   Web of Science ®Google Scholar