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State estimation of neural networks with time-varying delays and Markovian jumping parameter based on passivity theory

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Abstract

In this paper, the state estimation problem is investigated for neural networks with time-varying delays and Markovian jumping parameter based on passivity theory. The neural networks have a finite number of modes and the modes may jump from one to another according to a Markov chain. The main purpose is to estimate the neuron states, through available output measurements such that for all admissible time-delays, the dynamics of the estimation error is globally stable in the mean square and passive from the control input to the output error. Based on the new Lyapunov–Krasovskii functional and passivity theory, delay-dependent conditions are obtained in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate effectiveness of the proposed method and results.

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Acknowledgements

The work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0009373).

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Authors and Affiliations

  1. Nonlinear Dynamics Group, Department of Information and Communication Engineering/Electrical Engineering, Yeungnam University, 214-1 Dae-dong, Kyongsan, 712-749, Republic of Korea

    S. Lakshmanan, Ju H. Park & H. Y. Jung

  2. Mobile Communication Division, Digital Media and Communications, Samsung Electronics, Co. Ltd., Maetan-dong, Suwon, 416-2, Republic of Korea

    D. H. Ji

  3. Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram, 624 302, Tamilnadu, India

    G. Nagamani

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  1. S. Lakshmanan
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  2. Ju H. Park
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  3. D. H. Ji
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  4. H. Y. Jung
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  5. G. Nagamani
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Correspondence to Ju H. Park or H. Y. Jung.

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Lakshmanan, S., Park, J.H., Ji, D.H. et al. State estimation of neural networks with time-varying delays and Markovian jumping parameter based on passivity theory. Nonlinear Dyn 70, 1421–1434 (2012). https://doi.org/10.1007/s11071-012-0544-6

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  • DOI: https://doi.org/10.1007/s11071-012-0544-6

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