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Mean Square Exponential Stability of Stochastic Delayed Static Neural Networks with Markovian Switching

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Book cover Advances in Neural Networks – ISNN 2015 (ISNN 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9377))

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Abstract

This paper is concerned with globally exponential stability in the mean square of stochastic static neural networks with Markovian switching and time delay. Firstly, the mathematical model of this kind of recurrent neural networks is established by taking information latching and noise disturbance into consideration. Then, a stability condition, which is dependent on both time delay and system mode, is presented in terms of linear matrix inequalities. Based on it, the maximum value of the exponential decay rate can be efficiently found by solving a convex optimization problem.

This work was jointly supported by the National Natural Science Foundation of China under Grant Nos. 61273122 and 61005047, and the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2010214.

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References

  1. Boyd, S., EI Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)

    Book  MATH  Google Scholar 

  2. He, Y., Wang, Q.-G., Wu, M., Lin, C.: Delay-dependent state estimation for delayed neural networks. IEEE Trans. Neural Netw. 17, 1077–1081 (2006)

    Article  Google Scholar 

  3. Huang, H., Huang, T., Chen, X.: Global exponential estimates of delayed stochastic neural networks with Markovian switching. Neural Netw. 36, 136–145 (2012)

    Article  MATH  Google Scholar 

  4. Liu, Y., Wang, Z., Liu, X.: Stability analysis for a class of neutral-type neural networks with Markovian jumping parameters and mode-dependent mixed delays. Neurocomputing 94, 46–53 (2012)

    Article  Google Scholar 

  5. Mou, S., Gao, H., Lam, J., Qiang, W.: A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay. IEEE Trans. Neural Netw. 19, 532–535 (2008)

    Article  Google Scholar 

  6. Seung, H.S.: How the brain keeps the eye still. Proc. Natl. Acad. Sci. USA 93, 13339–13344 (1996)

    Article  Google Scholar 

  7. Seuret, A., Gouaisbaut, F.: Wirtinger-based integral inequality: application to time-delay systems. Automatica 49, 2860–2866 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Shao, L., Huang, H., Zhao, H., Huang, T.: Filter design of delayed static neural networks with Markovian jumping parameters. Neurocomputing 153, 126–132 (2015)

    Article  Google Scholar 

  9. Syed Ali, M., Marudaib, M.: Stochastic stability of discrete-time uncertain recurrent neural networks with Markovian jumping and time-varying delays. Math. Comput. Model. 54(9), 1979–1988 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Tan, H., Hua, M., Chen, J., Fei, J.: Stability analysis of stochastic Markovian switching static neural networks with asynchronous mode-dependent delays. Neurocomputing 151, 864–872 (2015)

    Article  Google Scholar 

  11. Tino, P., Cernansky, M., Benuskova, L.: Markovian architectural bias of recurrent neural networks. IEEE Trans. Neural Netw. 15, 6–15 (2004)

    Article  Google Scholar 

  12. Xu, Z.-B., Qiao, H., Peng, J., Zhang, B.: A comparative study of two modeling approaches in neural networks. Neural Netw. 17, 73–85 (2004)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Electronics and Information Engineering, Soochow University, Suzhou, 215006, P. R. China

    He Huang

Authors
  1. He Huang
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Correspondence to He Huang .

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Editors and Affiliations

  1. Department of Computer Science and Technology, Tsinghua University, Beijing, China

    Xiaolin Hu

  2. Fuzhou University, Fuzhou, China

    Yousheng Xia

  3. School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China

    Yunong Zhang

  4. Chinese Academy of Sciences, Institute of Automation, Beijing, China

    Dongbin Zhao

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Huang, H. (2015). Mean Square Exponential Stability of Stochastic Delayed Static Neural Networks with Markovian Switching. In: Hu, X., Xia, Y., Zhang, Y., Zhao, D. (eds) Advances in Neural Networks – ISNN 2015. ISNN 2015. Lecture Notes in Computer Science(), vol 9377. Springer, Cham. https://doi.org/10.1007/978-3-319-25393-0_16

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  • DOI: https://doi.org/10.1007/978-3-319-25393-0_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25392-3

  • Online ISBN: 978-3-319-25393-0

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