Robust analysis of discrete time noises for stochastic systems and application in neural networks

References

• Anbuvithya, R., Mathiyalagan, K., Sakthivel, R., & Prakash, P. (2016). Passivity of memristor-based BAM neural networks with different memductance and uncertain delays. Cognitive Neurodynamics, 10(4), 339–351.
   PubMed Web of Science ®Google Scholar
• Appleby, J. A. D., & Riedle, M. (2006). Almost sure asymptotic stability of stochastic Volterra integro-differential equations with fading perturbations. Stochastic Analysis and Applications, 24, 813–826.
   Web of Science ®Google Scholar
• Chen, W., Guan, Z., & Lu, X. (2005). Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: An LMI approach. Systems & Control Letters, 54, 547–555.
   Web of Science ®Google Scholar
• Feng, L., Li, S., Liu, Z., & Zheng, S. (2016). Robust stability of a class of stochastic functional differential equations with Markovian switching. Advances in Difference Equations, 2016(1), 205.
   Web of Science ®Google Scholar
• Feng, L., Wu, Z., & Zheng, S. (2018). A note on explosion suppression for nonlinear delay differential systems by polynomial noise. International Journal of General Systems, 47(2), 137–154.
   Web of Science ®Google Scholar
• Feng, J., & Xu, C. (2018). A graph-theoretic approach to exponential stability of stochastic complex networks with time-varying delays. Neurocomputing, 272, 453–460.
   Web of Science ®Google Scholar
• Haussmann, U. G. (1978). Asymptotic stability of the linear Itô equation in infinite dimensions. Journal of Mathematical Analysis and Applications, 65(1), 219–235.
   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, 178–187.
   Web of Science ®Google Scholar
• Hu, L., Mao, X., & Zhang, L. (2013). Robust stability and boundedness of nonlinear hybrid stochastic differential delay equations. IEEE Transactions on Automatic Control, 58, 2319–2332.
   Web of Science ®Google Scholar
• Hua, M., Tan, H., Fei, 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.
   Web of Science ®Google Scholar
• Hu, Y., Wu, F., & Huang, C. (2009). Robustness of exponential stability of a class of stochastic functional differential equations with infinite delay. Automatica, 45, 2577–2584.
   Web of Science ®Google Scholar
• Ichikawa, A. (1982). Stability of semilinear stochastic evolution equations. Journal of Mathematical Analysis and Applications, 90(1), 12–44.
   Web of Science ®Google Scholar
• Lei, J., & Mackey, M. C. (2007). Stochastic differential delay equation, moment stability, and application to hematopoietic stem cell regulation system. SIAM Journal on Applied Mathematics, 67(2), 387–407.
   Web of Science ®Google Scholar
• Li, R., Cao, J., Alsaedi, A., & Alsaadi, F. (2017). Exponential and fixed-time synchronization of Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms. Applied Mathematics and Computation, 313, 37–51.
   Web of Science ®Google Scholar
• Liu, L., Shen, Y., & Jiang, F. (2011). The almost sure asymptotic stability and pth moment asymptotic stability of nonlinear stochastic differential systems with polynomial growth. IEEE Transactions on Automatic Control, 56, 1985–1990.
   Web of Science ®Google Scholar
• Loeve, M. (1955). Probability theory: Foundations, random sequences. Princeton, NJ: van Nostrand.
   Google Scholar
• Luo, Q., Mao, X., & Shen, Y. (2011). Generalised theory on asymptotic stability and boundedness of stochastic functional differential equations. Automatica, 47, 2075–2081.
   Web of Science ®Google Scholar
• Mao, X. (1992). Robustness of stability of nonlinear systems with stochastic delay perturbations. Systems & Control Letters, 19, 391–400.
   Web of Science ®Google Scholar
• Mao, X. (2002). Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Transactions on Automatic Control, 47, 1604–1612.
   Web of Science ®Google Scholar
• Mao, X. (2007). Stochastic differential equations and applications (2nd ed.). Chichester: Horwood Publishing.
   Google Scholar
• Mao, X. (2016). Almost sure exponential stabilization by discrete-time stochastic feedback control. IEEE Transactions on Automatic Control, 61(6), 1619–1624.
   Web of Science ®Google Scholar
• Mao, X., Koroleva, N., & Rodkina, A. (1998). Robust stability of uncertain stochastic differential delay equations. Systems & Control Letters, 35, 325–336.
   Web of Science ®Google Scholar
• Mohajerpoor, R., Shanmugam, L., Abdi, H., Rakkiyappan, R., Nahavandi, S., & Park, J. H. (2017). Improved delay-dependent stability criteria for neutral systems with mixed interval time-varying delays and nonlinear disturbances. Journal of the Franklin Institute, 354(2), 1169–1194.
   Web of Science ®Google Scholar
• Pan, L., & Cao, J. (2012). Robust stability for uncertain stochastic neural network with delay and impulses. Neurocomputing, 94, 102–110.
   Web of Science ®Google Scholar
• Peng, S., & Yang, L. (2017). The pth moment boundedness of stochastic functional differential equations with Markovian switching. Journal of the Franklin Institute, 354(1), 345–359.
   Web of Science ®Google Scholar
• Shaikhet, L. (2017). Stability of equilibrium states of a nonlinear delay differential equation with stochastic perturbations. International Journal of Robust and Nonlinear Control, 27(6), 915–924.
   Web of Science ®Google Scholar
• Song, R., & Zhu, Q. (2018). Stability of linear stochastic delay differential equations with infinite Markovian switchings. International Journal of Robust and Nonlinear Control, 28(3), 825–837.
   Web of Science ®Google Scholar
• Tian, T., Burrage, K., Burrage, P. M., & Carletti, M. (2007). Stochastic delay differential equations for genetic regulatory networks. Journal of Computational and Applied Mathematics, 205(2), 696–707.
   Web of Science ®Google Scholar
• Wang, X., Jiang, M., & Fang, S. (2009). Stability analysis in lagrange sense for a nonautonomous Cohen-Grossberg neural network with mixed delays. Nonlinear Analysis: Theory, Methods & Applications, 70(12), 4294–4306.
   Web of Science ®Google Scholar
• Wang, Z., Shu, H., Fang, J., & Liu, X. (2006). Robust stability for stochastic Hopfield neural networks with time delays. Nonlinear Analysis: Real World Applications, 7(5), 1119–1128.
   Web of Science ®Google Scholar
• Wang, J., & Tian, L. (2017). Global lagrange stability for inertial neural networks with mixed time-varying delays. Neurocomputing, 235, 140–146.
   Web of Science ®Google Scholar
• Wang, B., & Zhu, Q. (2017). Stability analysis of Markov switched stochastic differential equations with both stable and unstable subsystems. Systems & Control Letters, 105, 55–61.
   Web of Science ®Google Scholar
• Wang, B., & Zhu, Q. (2018). Stability analysis of semi-Markov switched stochastic systems. Automatica, 94, 72–80.
   Web of Science ®Google Scholar
• Wu, F., & Hu, S. (2011). Attraction, stability and boundedness for stochastic functional differential equations with infinite delay. Automatica, 47, 2224–2232.
   Web of Science ®Google Scholar
• Wu, F., Hu, S., & Huang, C. (2010). Robustness of general decay stability of nonlinear neutral stochastic functional differential equations with infinite delay. Systems & Control Letters, 59, 195–202.
   Web of Science ®Google Scholar
• Yang, R., Gao, H., & Shi, P. (2009). Novel robust stability criteria for stochastic Hopfield neural networks with time delays. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 39(2), 467–474.
   PubMed Web of Science ®Google Scholar
• Yuan, C., & Mao, X. (2004). Robust stability and controllability of stochastic differential delay equations with Markovian switching. Automatica, 40, 343–354.
   Web of Science ®Google Scholar
• Yue, D., & Won, S. (2001). Delay-dependent robust stability of stochastic systems with time delay and nonlinear uncertainties. Electronics Letters, 37, 992–993.
   Web of Science ®Google Scholar
• Zhang, C., Li, W., Su, H., & Wang, K. (2014). Asymptotic boundedness for stochastic coupled systems on networks with Markovian switching. Neurocomputing, 136, 180–189.
   Web of Science ®Google Scholar
• Zhu, Q. (2017). Razumikhin-type theorem for stochastic functional differential equations with Lévy noise and Markov switching. International Journal of Control, 90(8), 1703–1712.
   Web of Science ®Google Scholar
• Zhu, Q. (2018). Stability analysis of stochastic delay differential equations with Lévy noise. Systems & Control Letters, 118, 62–68.
   Web of Science ®Google Scholar
• Zhu, Q., & Cao, J. (2010). Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Transactions on Neural Networks, 21(8), 1314–1325.
   PubMed Web of Science ®Google Scholar
• Zhu, Q., & Cao, J. (2012). Stability of Markovian jump neural networks with impulse control and time varying delays. Nonlinear Analysis: Real World Applications, 13(5), 2259–2270.
   Web of Science ®Google Scholar
• Zhu, Q., Cao, J., Hayat, T., & Alsaadi, F. (2015). Robust stability of Markovian jump stochastic neural networks with time delays in the leakage terms. Neural Processing Letters, 41(1), 1–27.
   Web of Science ®Google Scholar
• Zhu, F., Han, Z., & Zhang, J. (2014). Robust stability and stabilization of linear stochastic systems with Markovian switching and uncertain transition rates. Journal of Mathematical Analysis and Applications, 415, 677–685.
   Web of Science ®Google Scholar
• Zhu, Q., & Wang, H. (2018). Output feedback stabilization of stochastic feedforward systems with unknown control coefficients and unknown output function. Automatica, 87, 166–175.
   Web of Science ®Google Scholar
• Zhu, Q., & Zhang, Q. (2017). pth moment exponential stabilisation of hybrid stochastic differential equations by feedback controls based on discrete-time state observations with a time delay. IET Control Theory & Applications, 11(12), 1992–2003.
   Web of Science ®Google Scholar