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Articles

Stability of random impulsive coupled systems on networks with Markovian switching

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Pages 1107-1132 | Received 04 Nov 2018, Accepted 09 Jul 2019, Published online: 29 Jul 2019

References

  • Wang, J. L., Jiang, H. J., Hu, C., Ma, T. (2014). Convergence behavior of delayed discrete cellular neural network without periodic coefficients. Neural Netw. 53:61–68. DOI:10.1016/j.neunet.2014.01.007.
  • Cannas, B., Cincotti, S. (2002). Hyperchaotic behaviour of two bi-directionally coupled chua’s circuits. Int. J. Circ. Theor. Appl. 30(6):625–637. DOI:10.1002/cta.213.
  • Ji, L., Xu, W. G. (2008). Controlling the nonlinear chemical signal in a coupled system by delay. Chaos Solitons Fractals 36(5):1261–1266. DOI:10.1016/j.chaos.2006.07.048.
  • Liu, Y., Li, W. X., Feng, J. Q. (2018). Graph-theoretical method to the existence of stationary distribution of stochastic coupled systems. J. Dyn. Diff. Equat. 30(2):667–685. DOI:10.1007/s10884-016-9566-y.
  • Liu, K. C., Qu, Y. B., Kim, H. M., Song, H. H. (2018). Avoiding frequency second dip in power unreserved control during wind power rotational speed recovery. IEEE Trans. Power Syst. 33(3):3097–3106. DOI:10.1109/TPWRS.2017.2761897.
  • Li, M., Shuai, Z. S. (2010). Global-stability problem for coupled systems of differential equations on networks. J. Differ. Equ. 248(1):1–20. DOI:10.1016/j.jde.2009.09.003.
  • Lee, D. H., Joo, Y. H., Tak, M. H. (2013). Linear matrix inequality approach to local stability analysis of discrete-time Takagi-Sugeno fuzzy systems. IET Contr. Theory Appl. 7(9):1309–1318. DOI:10.1049/iet-cta.2013.0033.
  • Zhang, W. B., Tang, Y., Miao, Q. Y., Du, W. (2013). Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects. IEEE Trans. Neural Netw. Learn. Syst. 24(8):1316–1326. DOI:10.1109/TNNLS.2013.2257842.
  • Liu, B. (2008). Stability of solutions for stochastic impulsive systems via comparison approach. IEEE Trans. Automat. Contr. 53(9):2128–2133. DOI:10.1109/TAC.2008.930185.
  • Peng, S. G., Zhang, Y. (2010). Razumikhin-type theorems on p-th moment exponential stability of impulsive stochastic delay differential equations. IEEE Trans. Autom. Control 55(8):1917–1922. DOI:10.1109/TAC.2010.2049775.
  • Li, B., Li, D. S., Xu, D. Y. (2013). Stability analysis for impulsive stochastic delay differential equations with Markovian switching. J. Frankl. Inst. Eng. Appl. Math. 350(7):1848–1864. DOI:10.1016/j.jfranklin.2013.05.009.
  • Liu, Z. M., Peng, J. (2009). P-moment stability of stochastic nonlinear delay systems with impulsive jump and Markovian switching. Stoch. Anal. Appl. 27(5):911–923. DOI:10.1080/07362990903136439.
  • Wu, Z. J. (2015). Stability criteria of random nonlinear systems and their applications. IEEE Trans. Automat. Contr. 60(4):1038–1049. DOI:10.1109/TAC.2014.2365684.
  • Jiao, T., Lu, J., Li, Y., Chu, Y., Xu, S. (2016). Stability analysis of random systems with Markovian switching and its application. J. Frankl. Inst. Eng. Appl. Math. 353(1):200–220. DOI:10.1016/j.jfranklin.2015.10.012.
  • Jiao, T. C., Zong, G. D., Nguang, S. K., Zhang, C. S. (2019). Stability analysis of genetic regulatory networks with general random disturbances. IEEE Trans. Nanobiosci. 18(2):128–135. DOI:10.1109/TNB.2018.2887305.
  • Jiao, T. C., Zheng, W. X., Xu, S. Y. (2016). On stability of a class of switched nonlinear systems subject to random disturbances. IEEE Trans. Circuits Syst. I Pap. 63(12):2278–2289. DOI:10.1109/TCSI.2016.2620994.
  • Plonka, P. (2018). Some criteria for the existence of invariant measures and asymptotic stability for random dynamical systems on polish spaces. Stoch. Anal. Appl. 36(3):521–533. DOI:10.1080/07362994.2018.1428106.
  • Samojlenko, A., Stanzhytskyi, O. (2011). Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations. Singapore, DC: World Scientific.
  • Jiao, T. C., Zheng, W. X., Xu, S. Y. (2017). Stability analysis for a class of random nonlinear impulsive systems. Int. J. Robust Nonlinear Control 27(7):1171–1193. DOI:10.1002/rnc.3630.
  • Rakkiyappan, R., Balasubramaniam, P. (2009). Dynamic analysis of Markovian jumping impulsive stochastic Cohen-Grossberg neural networks with discrete interval and distributed time-varying delays. Nonlinear Anal.-Hybrid Syst. 3(4):408–417. DOI:10.1016/j.nahs.2009.02.008.
  • Yang, Y., Li, J. M., Chen, G. P. (2010). Finite-time stability and stabilization of Markovian switching stochastic systems with impulsive effects. J. Syst. Eng. Electron. 21(2):254–260. DOI:10.3969/j.issn.1004-4132.2010.02.014.
  • Xu, Y., He, Z. M. (2014). Stability of impulsive stochastic differential equations with Markovian switching. Appl. Math. Lett. 35:35–40. DOI:10.1016/j.aml.2014.04.008.
  • Zhu, Q. X. (2014). Pth moment exponential stability of impulsive stochastic functional differential equations with Markovian switching. J. Frankl. Inst. Eng. Appl. Math. 351(7):3965–3986. DOI:10.1016/j.jfranklin.2014.04.001.
  • Wu, X. T., Zhang, W. B., Tang, Y. (2013). Pth moment stability of impulsive stochastic delay differential systems with Markovian switching. Commun. Nonlinear Sci. Numer. Simul. 18(7):1870–1879. DOI:10.1016/j.cnsns.2012.12.001.
  • Chen, W. H., Zheng, W. X. (2009). Input-to-state stability and integral input-to-state stability of nonlinear impulsive systems with delays. Automatica 45(6):1481–1488. DOI:10.1016/j.automatica.2009.02.005.
  • Sun, X. M., Wang, W. (2012). Integral input-to-state stability for hybrid delayed systems with unstable continuous dynamics. Automatica 48(9):2359–2364. DOI:10.1016/j.automatica.2012.06.056.
  • West, D. (1996). Introduction to Graph Theory. Upper Saddle River: Prentice Hall.
  • Song, Z. G., Xu, J. (2012). Codimension-two bursting analysis in the delayed neural system with external stimulations. Nonlinear Dyn. 67(1):309–328. DOI:10.1007/s11071-011-9979-4.
  • Khasminskii, R. (2011). Stochastic Stability of Differential Equations. DC: Springer Science & Business Media.
  • Wang, P. F., Hong, Y., Su, H. (2018). Stabilization of stochastic complex-valued coupled delayed systems with Markovian switching via periodically intermittent control. Nonlinear Anal.-Hybrid Syst. 29:395–413. DOI:10.1016/j.nahs.2018.03.006.
  • Wu, Y. B., Yan, S. H., Fan, M., Li, W. X. (2018). Stabilization of stochastic coupled systems with Markovian switching via feedback control based on discrete-time state observations. Int. J. Robust Nonlinear Control 28(1):247–265. DOI:10.1002/rnc.3867.
  • Yao, L. Q., Zhang, W. H. (2018). Adaptive tracking control for a class of random pure-feedback nonlinear systems with Markovian switching. Int. J. Robust Nonlinear Control 28(8):3112–3126. DOI:10.1002/rnc.4071.
  • Li, D. Q., Cheng, P., He, S. P. (2017). Exponential stability of hybrid stochastic functional differential systems with delayed impulsive effects: average impulsive interval approach. Math. Meth. Appl. Sci. 40(11):4197–4210. DOI:10.1002/mma.4297.
  • Sobolev, V. S., Kashcheeva, G. A., Zhuravel, F. A. (2017). Maximum likelihood estimates of the Central frequency of narrow-band random normal processes from a minimum number of samples. J. Commun. Technol. Electron. 62(9):990–1003. DOI:10.1134/S1064226917090182.
  • Jiao, T. C., Zong, G. D., Zhang, C. S., Du, Q. J., Zhao, Y. L. (2018). Noise-to-state stability analysis for a class of random time-delay nonlinear systems. Trans. Inst. Meas. Control 40(9):2765–2770. DOI:10.1177/0142331217750223.

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