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Exponential Stability for Delayed Stochastic Bidirectional Associative Memory Neural Networks with Markovian Jumping and Impulses

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Abstract

In this paper, the problem of stability analysis for a class of delayed stochastic bidirectional associative memory neural network with Markovian jumping parameters and impulses are being investigated. The jumping parameters assumed here are continuous-time, discrete-state homogeneous Markov chain and the delays are time-variant. Some novel criteria for exponential stability in the mean square are obtained by using a Lyapunov function, Ito’s formula and linear matrix inequality optimization approach. The derived conditions are presented in terms of linear matrix inequalities. The estimate of the exponential convergence rate is also given, which depends on the system parameters and impulsive disturbed intension. In addition, a numerical example is given to show that the obtained result significantly improve the allowable upper bounds of delays over some existing results.

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Authors and Affiliations

  1. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, South Korea

    R. Sakthivel

  2. Department of Mathematics, Periyar University, Salem, 636-011, India

    R. Raja

  3. Department of Mathematics, Anna University Coimbatore, Coimbatore, 641-047, India

    S. M. Anthoni

Authors
  1. R. Sakthivel
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  2. R. Raja
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  3. S. M. Anthoni
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Corresponding author

Correspondence to R. Sakthivel.

Additional information

Communicated by Qianchuan Zhao.

The work of R. Sakthivel was supported by the Korean Research Foundation Grant funded by the Korean Government with grant number KRF 2010-0003495. The work of R. Raja was supported by UGC Rajiv Gandhi National Fellowship and the work of S.M. Anthoni was supported by the CSIR, New Delhi.

"This article is an unintentional duplicate of another article in this journal, by the same authors, which should be considered the version of record and used for citation purposes: R.Sakthivel, R.Raja, S. M.Anthoni, Exponential Stability for Delayed Stochastic Bidirectional Associative Memory Neural Networks with Markovian Jumping and Impulses, Journal of Optimization Theory and Applications, Volume 150, Issue 1, pages 166-187, http://dx.doi.org/10.1007/s10957-011-9808-4.apologizes to the readers of the journal for not detecting the duplication during the publishing process."

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Sakthivel, R., Raja, R. & Anthoni, S.M. Exponential Stability for Delayed Stochastic Bidirectional Associative Memory Neural Networks with Markovian Jumping and Impulses. J Optim Theory Appl 158, 251–273 (2013). https://doi.org/10.1007/s10957-011-9817-3

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  • DOI: https://doi.org/10.1007/s10957-011-9817-3

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