52
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

Instability of stochastic differential systems with impulsive effects

, &
Pages 1810-1818 | Received 16 Jun 2022, Accepted 28 Jun 2023, Published online: 19 Jul 2023

References

  • Ahmad, B., & Sivasundaram, S. (2010). Instability criteria for impulsive hybrid state dependent delay integrodifferential systems. Nonlinear Analysis: Real World Applications, 11(2), 750–758. https://doi.org/10.1016/j.nonrwa.2009.01.011
  • Cao, W. P., & Zhu, Q. X. (2021). Razumikhin-type theorem for pth exponential stability of impulsive stochastic functional differential equations based on vector Lyapunov function. Nonlinear Analysis: Hybrid Systems, 39, Article 100983, 10 pp. https://doi.org/10.1016/j.nahs.2020.100983
  • Chen, S. Y., Feng, J. W., Wang, J. Y., & Zhao, Y. (2020). Almost sure exponential synchronization of drive-response stochastic memristive neural networks. Applied Mathematics and Computation, 383, Article 125360, 15 pp. https://doi.org/10.1016/j.amc.2020.125360
  • Cheng, P., Deng, F. Q., & Yao, F. Q. (2018). Almost sure exponential stability and stochastic stabilization of stochastic differential systems with impulsive effects. Nonlinear Analysis: Hybrid Systems, 30, 106–117. https://doi.org/10.1016/j.nahs.2018.05.003
  • El Fatini, M., Lahrouz, A., Pettersson, R., Settati, A., & Taki, R. (2018). Stochastic stability and instability of an epidemic model with relapse. Applied Mathematics and Computation, 316, 326–341. https://doi.org/10.1016/j.amc.2017.08.037
  • Feng, L. C., Wu, Z. H., Cao, J. D., Zheng, S. Q., & Alsaadi, F. E. (2020). Exponential stability for nonlinear hybrid stochastic systems with time varying delays of neutral type. Applied Mathematics Letters, 107, Article 106468, 9 pp. https://doi.org/10.1016/j.aml.2020.106468
  • Guo, Y., Lin, W., Chen, Y. M., & J. H. Wu (2017). Instability in time-delayed switched systems induced by fast and random switching. Journal of Differential Equations, 263(2), 880–909. https://doi.org/10.1016/j.jde.2017.03.003
  • Guo, Y. X., Zhu, Q. X., & Wang, F. (2020). Stability analysis of impulsive stochastic functional differential equations. Communications in Nonlinear Science and Numerical Simulation, 82, Article 105013, 12 pp. https://doi.org/10.1016/j.cnsns.2019.105013
  • Hu, W., & Zhu, Q. X. (2020). Stability analysis of impulsive stochastic delayed differential systems with unbounded delays. Systems & Control Letters, 136, Article 104606, 7 pp. https://doi.org/10.1016/j.sysconle.2019.104606
  • Li, B. (2018). Stability of stochastic functional differential equations with impulses by an average approach. Nonlinear Analysis: Hybrid Systems, 29, 221–233. https://doi.org/10.1016/j.nahs.2018.02.002
  • Li, C. X. (2021). Stability of stochastic delay differential systems with variable impulses due to logic choice. IEEE Access, 9, 81546–81553. https://doi.org/10.1109/ACCESS.2021.3085757
  • Li, S., Ahn, C. K., & Xiang, Z. R. (2019). Sampled-data adaptive output feedback fuzzy stabilization for switched nonlinear systems with asynchronous switching. IEEE Transactions on Fuzzy Systems, 27(1), 200–205. https://doi.org/10.1109/TFUZZ.2018.2881660
  • Li, X. D., Chen, W. H., Zheng, W. X., & Wang, Q. G. (2018). Instability and unboundedness analysis for impulsive differential systems with applications to Lurie control systems. International Journal of Control, Automation and Systems, 16(4), 1521–1531. https://doi.org/10.1007/s12555-017-0609-x
  • Liu, K. (2018). Almost sure exponential stability sensitive to small time delay of stochastic neutral functional differential equations. Applied Mathematics Letters, 77, 57–63. https://doi.org/10.1016/j.aml.2017.09.008
  • Lu, X. D., & Zhang, X. F. (2019). Stability analysis of switched systems on time scales with all modes unstable. Nonlinear Analysis: Hybrid Systems, 33, 371–379. https://doi.org/10.1016/j.nahs.2019.04.002
  • Ma, Y. J., & Sun, J. T. (2007). Stability criteria of delay impulsive systems on time scales. Nonlinear analysis. Nonlinear Analysis: Theory Methods & Applications, 67(4), 1181–1189. https://doi.org/10.1016/j.na.2006.07.006
  • Mao, X. R. (2007). Stochastic differential equations and applications. Horwood Publishing.
  • Mei, W. J., & Ogura, M. (2019). Kronecker weights for instability analysis of Markov jump linear systems. IET Control Theory & Applications, 13(3), 360–366. https://doi.org/10.1049/cth2.v13.3
  • Wang, J. Y., Feng, J. W., Lou, Y. J., & Chen, G. R. (2021). Synchronization of networked harmonic oscillators via quantized sampled velocity feedback. IEEE Transactions on Automatic Control, 66(7), 3267–3273. https://doi.org/10.1109/TAC.2020.3014905
  • Wei, T. D., Lin, P., Zhu, Q. X., & Yao, Q. (2021). Instability of impulsive stochastic systems with application to image encryption. Applied Mathematics and Computation, 402, Article 126098, 13 pp. https://doi.org/10.1016/j.amc.2021.126098
  • Wu, X. T., Tang, Y., & Zhang, W. B. (2016). Input-to-state stability of impulsive stochastic delayed systems under linear assumptions. Automatica, 66, 195–204. https://doi.org/10.1016/j.automatica.2016.01.002
  • Xu, Y., & He, Z. M. (2016). Exponential stability of neutral stochastic delay differential equations with Markovian switching. Applied Mathematics Letters, 52, 64–73. https://doi.org/10.1016/j.aml.2015.08.019
  • Yang, Y., He, Y., Wang, Y., & Wu, M. (2017). Stability analysis for impulsive fractional hybrid systems via variational Lyapunov method. Communications in Nonlinear Science and Numerical Simulation, 45, 140–157. https://doi.org/10.1016/j.cnsns.2016.09.009
  • Yin, J. L., Khoo, S., & Yu, X. H. (2011). Finite-time stability and instability of stochastic nonlinear systems. Automatica, 47(12), 2671–2677. https://doi.org/10.1016/j.automatica.2011.08.050
  • Zhang, H., & Y. Q. Xia (2015). Instability of stochastic switched systems. Systems & Control Letters, 75, 101–107. https://doi.org/10.1016/j.sysconle.2014.10.007

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.