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Design of sampled data state estimator for Markovian jumping neural networks with leakage time-varying delays and discontinuous Lyapunov functional approach

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Abstract

This paper is concerned with the sampled-data state estimation problem for neural networks with both Markovian jumping parameters and leakage time-varying delays. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. In order to make full use of the sawtooth structure characteristic of the sampling input delay, a discontinuous Lyapunov functional is proposed based on the extended Wirtinger inequality. A less conservative delay dependent stability criterion is derived via constructing a new triple-integral Lyapunov–Krasovskii functional and the famous Jenson integral inequality. Based on the Lyapunov–Krasovskii functional approach, a state estimator of the considered neural networks has been achieved by solving some linear matrix inequalities, which can be easily facilitated by using the standard numerical software. Finally, two numerical examples are provided to show the effectiveness of the proposed methods.

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Acknowledgements

The work of R. Rakkiyappan was supported by NBHM Research Project under the sanctioned No: 2/48(7)/2012/NBHM(R.P.)/R and D II/12669 and Quanxin Zhu’s work was jointly supported by the National Natural Science Foundation of China (10801056), the Natural Science Foundation of Zhejiang Province (LY12F03010) and the Natural Science Foundation of Ningbo (2012A610032).

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Authors and Affiliations

  1. Department of Mathematics, Bharathiar University, Coimbatore, 641046, Tamilnadu, India

    R. Rakkiyappan & T. Radhika

  2. School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing, 210023, Jiangsu, China

    Quanxin Zhu

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  1. R. Rakkiyappan
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  2. Quanxin Zhu
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  3. T. Radhika
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Correspondence to Quanxin Zhu.

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Rakkiyappan, R., Zhu, Q. & Radhika, T. Design of sampled data state estimator for Markovian jumping neural networks with leakage time-varying delays and discontinuous Lyapunov functional approach. Nonlinear Dyn 73, 1367–1383 (2013). https://doi.org/10.1007/s11071-013-0870-3

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  • DOI: https://doi.org/10.1007/s11071-013-0870-3

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