Research Article
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Year 2020, Volume: 69 Issue: 2, 1285 - 1309, 31.12.2020
https://doi.org/10.31801/cfsuasmas.769920

Abstract

References

  • Haykin, S., Neural Networks: A Comprehensive Foundation, Prentice Hall, NJ, 1998.
  • Arik, S., Stability analysis of delayed neural networks, IEEE Transactions on Circuits and Systems, I 47 (1997), 1089-1092.
  • Liu, Y. R., Wang, Z. D., Liu, X., Global exponential stability of generalized recurrent neural networks with discrete and distributed delays, Neural Networks, 19 (2006), 667-675.
  • Zhang, Q., Wei, X., Xu, J., Delay-dependent global stability condition for delayed Hopfield neural networks, Nonlinear Analysis: Real World Applications, 8 (2007), 997-1002.
  • Wu, H., Feng, W., Liang, X., New stability criteria for uncertain neural networks with interval time-varying delays, Cognitive Neurodynamics, 2 (2008), 363-370.
  • Li, X., Chen, Z., Stability properties for Hopfield neural networks with delays and impulsive perturbations, Nonlinear Analysis: Real World Applications, 10 (2009), 3253-3265.
  • Shao, H., Novel delay-dependent stability results for neural networks with time-varying delays, Circuits Systems and Signal Processings, 29 (2010), 637-647.
  • Chen, W.H., Lu, X., Mean square exponential stability of uncertain stochastic delayed neural networks, Physics Letters A, 372 (2008), 1061-1069.
  • Feng, W., Yang, S. X., Wu, H., On robust stability of uncertain stochastic neural networks with distributed and interval time-varying delays, Chaos, Solitons and Fractals, 42 (2009), 2095-2104.
  • Ma, L., Da, F., Mean-square exponential stability of stochastic Hopfield neural networks with time-varying discrete and distributed delays, Physics Letters A, 373 (2009), 2154-2161.
  • Lou, X., Cui, B., Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters, Journal of Mathematical Analysis and Applications, 328 (2007), 316-326.
  • Rakkiyappan, R., Balasubramaniam, P., Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays, Applied Mathematics and Computation, 198 (2008), 526-533.
  • Zhou, Q., Wan, L., Exponential stability of stochastic delayed Hopfield neural networks, Applied Mathematics and Computation, 199 (2008), 84-89.
  • Sakthivel, R., Samidurai, R., Anthoni, S.M., Asymptotic stability of stochastic delayed recurrent neural networks with impulsive effects, Journal of Optimization Thoery and Applications, 147 (2010), 583-596.
  • Sakthivel, R., Samidurai, R., Anthoni, S.M., New exponential stability criteria for stochastic BAM neural networks with impulses, Physica Scripta, 82 (2010), 045802.
  • Sakthivel, R., Raja, R., Anthoni, S.M., Asymptotic stability of delayed stochastic genetic regulatory networks with impulses, Physica Scripta, 82 (2010), 055009.
  • Zhang, Y. J., Yue, D., Tian, E. G., Robust delay-distribution-dependent stability of discrete-time stochastic neural networks with time-varying delay, Neurocomputing, 72 (2009), 1265-1273.
  • Fu, J., Zhang, H. G., Ma, T., Delay-probablity-distribution-dependent robust stability analysis for stochastic neural networks with time-varying delays, Progress Natural Science, 19 (2009), 1333-1340.
  • Takagi, T., Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on System, Man, and Cybernetics, 15 (1985), 116-132.
  • Huang, H., Ho, D.W.C., Lam, J., Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays, IEEE Transactions on Circuits and Systems, II 52 (2005) 251-255.
  • Li, H., Chen, B., Lin, C., Zhou, Q., Mean square exponential stability of stochastic fuzzy Hopfield neural networks with discrete and distributed time-varying delays, Neurocomputing, 72 (2009) 2017-2023.
  • Sheng, L., Gao, M., Yang, H., Delay-dependent robust stability for uncertain stochastic fuzzy Hopfield neural networks with time-varying delays, Fuzzy Sets and Systems, 160 (2009), 3503-3517.
  • Rakkiyappan, R., Balasubramaniam, P., Delay-probability-distribution-dependent stability of uncertain stochastic genetic regulatory networks with mixed time-varying delays: An LMI approach, Nonlinear Analysis: Hybrid Systems, 4 (2010), 600-607.
  • Gu, K., Integral inequality in the stability problem of time-delay Systems, Proceeding 39th IEEE CDC, Sydney, Philadelphia, 1994.
  • Boyd, S., Ghaoui, L. E., Feron, E., Balakrishnan, V., Linear Matrix Inequalities in Systems and Control Theory, SIAM books, Philadelphia, 1994.
  • Xie, L., Output feedback H_{∞} control of systems with parameter uncertainty, International Journal of Control, 63(1996)741-750.
  • Moon, Y.S., Park, P., Kwon, W.H., Lee, Y.S., Delay-dependent robust stabilization of uncertain state-delayed systems, International Journal of Control, 74 (2001), 1447-1455.

Robust stability analysis for fuzzy stochastic Hopfield neural networks with time–varying delays

Year 2020, Volume: 69 Issue: 2, 1285 - 1309, 31.12.2020
https://doi.org/10.31801/cfsuasmas.769920

Abstract

This paper investigates the delay-dependent robust stability problem of fuzzy stochastic Hopfield neural networks with random timevarying delays. Moreover, in this paper, the stochastic delay is assumed to satisfy a certain probability distribution. By introducing a stochastic variable with Bernoulli distribution, the neural networks with random time delays is transformed into one with deterministic delays and stochastic parameters. Based on a LyapunovKrasovskii functional and stochastic analysis approach, delay-probability-distribution-dependent stability criteria have been derived in terms of linear matrix inequalities (LMIs), which can be checked easily by the LMI control toolbox. Finally two numerical examples are given to illustrate the effectiveness of the theoretical results.

References

  • Haykin, S., Neural Networks: A Comprehensive Foundation, Prentice Hall, NJ, 1998.
  • Arik, S., Stability analysis of delayed neural networks, IEEE Transactions on Circuits and Systems, I 47 (1997), 1089-1092.
  • Liu, Y. R., Wang, Z. D., Liu, X., Global exponential stability of generalized recurrent neural networks with discrete and distributed delays, Neural Networks, 19 (2006), 667-675.
  • Zhang, Q., Wei, X., Xu, J., Delay-dependent global stability condition for delayed Hopfield neural networks, Nonlinear Analysis: Real World Applications, 8 (2007), 997-1002.
  • Wu, H., Feng, W., Liang, X., New stability criteria for uncertain neural networks with interval time-varying delays, Cognitive Neurodynamics, 2 (2008), 363-370.
  • Li, X., Chen, Z., Stability properties for Hopfield neural networks with delays and impulsive perturbations, Nonlinear Analysis: Real World Applications, 10 (2009), 3253-3265.
  • Shao, H., Novel delay-dependent stability results for neural networks with time-varying delays, Circuits Systems and Signal Processings, 29 (2010), 637-647.
  • Chen, W.H., Lu, X., Mean square exponential stability of uncertain stochastic delayed neural networks, Physics Letters A, 372 (2008), 1061-1069.
  • Feng, W., Yang, S. X., Wu, H., On robust stability of uncertain stochastic neural networks with distributed and interval time-varying delays, Chaos, Solitons and Fractals, 42 (2009), 2095-2104.
  • Ma, L., Da, F., Mean-square exponential stability of stochastic Hopfield neural networks with time-varying discrete and distributed delays, Physics Letters A, 373 (2009), 2154-2161.
  • Lou, X., Cui, B., Delay-dependent stochastic stability of delayed Hopfield neural networks with Markovian jump parameters, Journal of Mathematical Analysis and Applications, 328 (2007), 316-326.
  • Rakkiyappan, R., Balasubramaniam, P., Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays, Applied Mathematics and Computation, 198 (2008), 526-533.
  • Zhou, Q., Wan, L., Exponential stability of stochastic delayed Hopfield neural networks, Applied Mathematics and Computation, 199 (2008), 84-89.
  • Sakthivel, R., Samidurai, R., Anthoni, S.M., Asymptotic stability of stochastic delayed recurrent neural networks with impulsive effects, Journal of Optimization Thoery and Applications, 147 (2010), 583-596.
  • Sakthivel, R., Samidurai, R., Anthoni, S.M., New exponential stability criteria for stochastic BAM neural networks with impulses, Physica Scripta, 82 (2010), 045802.
  • Sakthivel, R., Raja, R., Anthoni, S.M., Asymptotic stability of delayed stochastic genetic regulatory networks with impulses, Physica Scripta, 82 (2010), 055009.
  • Zhang, Y. J., Yue, D., Tian, E. G., Robust delay-distribution-dependent stability of discrete-time stochastic neural networks with time-varying delay, Neurocomputing, 72 (2009), 1265-1273.
  • Fu, J., Zhang, H. G., Ma, T., Delay-probablity-distribution-dependent robust stability analysis for stochastic neural networks with time-varying delays, Progress Natural Science, 19 (2009), 1333-1340.
  • Takagi, T., Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on System, Man, and Cybernetics, 15 (1985), 116-132.
  • Huang, H., Ho, D.W.C., Lam, J., Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays, IEEE Transactions on Circuits and Systems, II 52 (2005) 251-255.
  • Li, H., Chen, B., Lin, C., Zhou, Q., Mean square exponential stability of stochastic fuzzy Hopfield neural networks with discrete and distributed time-varying delays, Neurocomputing, 72 (2009) 2017-2023.
  • Sheng, L., Gao, M., Yang, H., Delay-dependent robust stability for uncertain stochastic fuzzy Hopfield neural networks with time-varying delays, Fuzzy Sets and Systems, 160 (2009), 3503-3517.
  • Rakkiyappan, R., Balasubramaniam, P., Delay-probability-distribution-dependent stability of uncertain stochastic genetic regulatory networks with mixed time-varying delays: An LMI approach, Nonlinear Analysis: Hybrid Systems, 4 (2010), 600-607.
  • Gu, K., Integral inequality in the stability problem of time-delay Systems, Proceeding 39th IEEE CDC, Sydney, Philadelphia, 1994.
  • Boyd, S., Ghaoui, L. E., Feron, E., Balakrishnan, V., Linear Matrix Inequalities in Systems and Control Theory, SIAM books, Philadelphia, 1994.
  • Xie, L., Output feedback H_{∞} control of systems with parameter uncertainty, International Journal of Control, 63(1996)741-750.
  • Moon, Y.S., Park, P., Kwon, W.H., Lee, Y.S., Delay-dependent robust stabilization of uncertain state-delayed systems, International Journal of Control, 74 (2001), 1447-1455.
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Gopalakrishnan N 0000-0002-2365-9305

Publication Date December 31, 2020
Submission Date July 15, 2020
Acceptance Date August 20, 2020
Published in Issue Year 2020 Volume: 69 Issue: 2

Cite

APA N, G. (2020). Robust stability analysis for fuzzy stochastic Hopfield neural networks with time–varying delays. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1285-1309. https://doi.org/10.31801/cfsuasmas.769920
AMA N G. Robust stability analysis for fuzzy stochastic Hopfield neural networks with time–varying delays. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2020;69(2):1285-1309. doi:10.31801/cfsuasmas.769920
Chicago N, Gopalakrishnan. “Robust Stability Analysis for Fuzzy Stochastic Hopfield Neural Networks With time–varying Delays”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 2 (December 2020): 1285-1309. https://doi.org/10.31801/cfsuasmas.769920.
EndNote N G (December 1, 2020) Robust stability analysis for fuzzy stochastic Hopfield neural networks with time–varying delays. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1285–1309.
IEEE G. N, “Robust stability analysis for fuzzy stochastic Hopfield neural networks with time–varying delays”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 2, pp. 1285–1309, 2020, doi: 10.31801/cfsuasmas.769920.
ISNAD N, Gopalakrishnan. “Robust Stability Analysis for Fuzzy Stochastic Hopfield Neural Networks With time–varying Delays”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (December 2020), 1285-1309. https://doi.org/10.31801/cfsuasmas.769920.
JAMA N G. Robust stability analysis for fuzzy stochastic Hopfield neural networks with time–varying delays. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1285–1309.
MLA N, Gopalakrishnan. “Robust Stability Analysis for Fuzzy Stochastic Hopfield Neural Networks With time–varying Delays”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 2, 2020, pp. 1285-09, doi:10.31801/cfsuasmas.769920.
Vancouver N G. Robust stability analysis for fuzzy stochastic Hopfield neural networks with time–varying delays. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1285-309.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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