Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
distributed delays; leakage delay; passivity impulses; stochastic disturbances
distributed delays; leakage delay; passivity impulses; stochastic disturbances
Summary:
In this paper, the problem of passivity analysis for a class of uncertain stochastic neural networks with mixed delays and impulsive control is investigated. The mixed delays include constant delay in the leakage term, discrete and distributed delays. The discrete delays are assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By using Lyapunov stability theory, stochastic analysis, linear matrix inequality techniques and introducing some free-weighting matrices, several novel sufficient conditions are derived to guarantee the passivity of the suggested system in the sense of mean square under two cases: with known or unknown parameters. It is believed that these results are significant and useful for the design and applications of impulsive stochastic neural networks. Finally, two numerical examples are provided to show the effectiveness of the theoretical results.
References:
[1] Balasubramaniam, P., Nagamani, G., Rakkiyappan, R.: Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term. Comm. Nonlinear Sci. Numerical Simul. 16 (2011), 4422-4437. DOI 10.1016/j.cnsns.2011.03.028 | MR 2806757
[2] Boyd, S., Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia 1994. DOI 10.1137/1.9781611970777 | Zbl 0816.93004
[3] Cao, J., Li, R.: Fixed-time synchronization of delayed memristor-based recurrent neural networks. Science China Inform. Sci. 60 (2017), 032201. DOI 10.1007/s11432-016-0555-2
[4] Cao, J., Rakkiyappan, R., Maheswari, K., Chandrasekar, A.: Exponential $H_{\infty}$ filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities. Science China Inform. Sci. 59(2016), 3, 387-402. DOI 10.1007/s11431-016-6006-5
[5] Chen, Y., Wang, H., Xue, A., Lu, R.: Passivity analysis of stochastic time-delay neural networks. Nonlinear Dynamics 61 (2010), 71-82. DOI 10.1007/s11071-009-9632-7 | MR 2661785
[6] Gopalsamy, K.: Stability and Oscillations in Delay Differential Equations of Population Dynamics. Kluwer Academic Publishers, Dordrecht 1992. DOI 10.1007/978-94-015-7920-9 | MR 1163190
[7] Haykin, S.: Neural Networks: a Comprehensive Foundation (revised ed.). Upper Saddle River, Prentice-Hall, NJ 1998.
[8] Hu, M., Cao, J., Hu, A.: Exponential stability of discrete-time recurrent neural networks with time-varying delays in the leakage terms and linear fractional uncertainties. IMA J. Math. Control Inform. 31 (2014), 345-362. DOI 10.1093/imamci/dnt014 | MR 3264991
[9] Gu, K.: An integral inequality in the stability problem of time delay systems. In: Proc. 39th IEEE Conference on Decision Control 2000, pp. 2805-2810. DOI 10.1109/cdc.2000.914233
[10] He, Y., Wang, Q., Lin, C., Wu, M.: Delay-range-dependent stability for systems with time-varying delay. Automatica 43 (2007), 371-376. DOI 10.1016/j.automatica.2006.08.015 | MR 2281843
[11] Kwon, O., Lee, S., Park, Ju H.: Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays. Physics Lett. A 374 (2010), 1232-1241. DOI 10.1016/j.physleta.2010.01.007
[12] Kwon, O., Park, M., Park, Ju.H., Lee, S., Cha, E.: Improved approaches to stability criteria for neural networks with time-varying delays. J. Franklin Inst. 350 (2013), 2710-2735. DOI 10.1016/j.jfranklin.2013.06.014 | MR 3146943
[13] Li, X., Cao, J.: Delay-dependent stability of neural networks of neutral typewith time delay in the leakage term. Nonlinearity 23 (2010), 1709-1726. DOI 10.1088/0951-7715/23/7/010 | MR 2652478
[14] Li, R., Cao, J.: Dissipativity analysis of memristive neural networks with time-varying delays and randomly occurring uncertainties. Math. Methods Appl. Sci. 39 (2016), 11, 2896-2915. DOI 10.1002/mma.3738 | MR 3512738
[15] Li, R., Cao, J.: Stability analysis of reaction-diffusion uncertain memristive neural networks with time-varying delays and leakage term. Appl. Math. Comput. 278 (2016), 54-69. DOI 10.1016/j.amc.2016.01.016 | MR 3457642
[16] Li, X., Fu, X.: Effect of leakage time-varying delay on stability of nonlinear differential systems. J. Franklin Inst. 350 (2013), 1335-1344. DOI 10.1016/j.jfranklin.2012.04.007 | MR 3067559
[17] Li, X., Rakkiyappan, R.: Stability results for Takagi-Sugeno fuzzy uncertain BAM neural networks with time delays in the leakage term. Neural Computing Appl. 22 (2013), S203-S219. DOI 10.1007/s00521-012-0839-z
[18] Li, X., Song, S.: Impulsive control for existence, uniqueness and global stability of periodic solutions of recurrent neural networks with discrete and continuously distributed delays. IEEE Trans. Neural Networks Learning Systems 24 (2013), 868-877. DOI 10.1109/tnnls.2012.2236352
[19] Li, X., Song, S.: Stabilization of delay systems: Delay-dependent impulsive control. IEEE Trans. Automat. Control 62 (2017), 406-411. DOI 10.1109/tac.2016.2530041
[20] Li, H., Wang, C., Shi, P., Gao, H.: New passivity results for uncertain discrete-time stochastic neural networks with mixed time delays. Neurocomputing 73 (2010), 3291-3299. DOI 10.1016/j.neucom.2010.04.019
[21] Li, X., Wu, J.: Stability of nonlinear differential systems with state-dependent delayed impulses. Automatica 64 (2016), 63-69. DOI 10.1016/j.automatica.2015.10.002
[22] Li, Y., Yang, L., Sun, L.: Existence and exponential stability of an equilibrium point for fuzzy BAM neural networks with time-varying delays in leakage terms on time scales. Advances Diff. Equations 2013 (2013), 218. DOI 10.1186/1687-1847-2013-218
[23] Liu, Y., D.Wang, Z., Liu, X. H.: Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Networks 19 (2006), 5, 667-675. DOI 10.1016/j.neunet.2005.03.015
[24] Mao, X.: Stochastic Differential Equations with their Applications. Horwood, Chichester 1997.
[25] Michel, A., Liu, D.: Qualitative Analysis and Synthesis of Recurrent Neural Networks. Marcel Dekker, New York 2002.
[26] Pan, L., Cao, J.: Robust stability for uncertain stochastic neural network with delay and impulses. Neurocomputing 94 (2012), 102-110. DOI 10.1016/j.neucom.2012.04.013
[27] Raja, R., Raja, U. Karthik, Samidurai, R., Leelamani, A.: Dissipativity of discrete-time BAM stochastic neural networks with Markovian switching and impulses. J. Franklin Inst. 350 (2013), 3217-3247. DOI 10.1016/j.jfranklin.2013.08.003 | MR 3123415
[28] Raja, R., Raja, U. Karthik, Samidurai, R., Leelamani, A.: Passivity analysis for uncertain discrete time stochastic BAM neural networks with time-varying delays. Neural Computing Appl. 25 (2014), 751-766. DOI 10.1007/s00521-014-1545-9
[29] Raja, R., Samidurai, R.: New delaydependent robust asymptotic stability for uncertain stochastic recurrent neural networks with multiple time varying delays. J. Franklin Inst. 349 (2012), 2108-2123. DOI 10.1016/j.jfranklin.2012.03.007 | MR 2935279
[30] Rubio, J.: Interpolation neural network model of a manufactured wind turbine. Neural Computing Appl. 28 (2017), 2017-2028. DOI 10.1007/s00521-015-2169-4
[31] Song, Q., Cao, J.: Passivity of uncertain neural networks with both leakage delay and time-varying delay. Nonlinear Dynamics 67 (2012), 1695-1707. DOI 10.1007/s11071-011-0097-0 | MR 2870615
[32] Song, Q., Cao, J.: Passivity of uncertain neural networks with both leakage delay and time-varying delay. Nonlinear Dynamics 67 (2012), 1695-1707. DOI 10.1007/s11071-011-0097-0 | MR 2870615
[33] Tu, Z., Cao, J., Alsaedi, A., Hayat, T: Global dissipativity analysis for delayed quaternion-valued neural networks. Neural Networks 89 (2017), 97-104. DOI 10.1016/j.neunet.2017.01.006
[34] Wu, Z., Park, Ju H., Su, H., Chu, J.: New results on exponential passivity of neural networks with time-varying delays. Nonlinear Analysis: Real World Appl. 13 (2012), 1593-1599. DOI 10.1016/j.nonrwa.2011.11.017 | MR 2890995
[35] Yang, C., Huang, T.: Improved stability criteria for a class of neural networks with variable delays and impulsive perturbations. Appl. Math. Comput. 243 (2014), 923-935. DOI 10.1016/j.amc.2014.06.045
[36] Zhao, Z., Song, Q., He, S.: Passivity analysis of stochastic neural networks with time-varying delays and leakage delay. Neurocomputing 47 (2015), 1-10. DOI 10.1016/j.neucom.2012.08.049
[37] Zheng, C., Gong, C., Wang, Z.: New passivity conditions with fewer slack variables for uncertain neural networks with mixed delays. Neurocomputing 118 (2013), 237-244. DOI 10.1016/j.neucom.2013.02.032
Search
Partner of
