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Sampled-Data State Estimation for Neural Networks with Additive Time–Varying Delays

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Abstract

In this paper, we consider the problem of delay-dependent stability for state estimation of neural networks with two additive time–varying delay components via sampled-data control. By constructing a suitable Lyapunov–Krasovskii functional with triple and four integral terms and by using Jensen’s inequality, a new delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs) to ensure the asymptotic stability of the equilibrium point of the considered neural networks. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. Due to the delay-dependent method, a significant source of conservativeness that could be further reduced lies in the calculation of the time-derivative of the Lyapunov functional. The relationship between the time-varying delay and its upper bound is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some less conservative stability criteria are established for systems with two successive delay components. Finally, numerical example is given to show the superiority of proposed method.

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Authors and Affiliations

  1. Department of Mathematics, Thiruvalluvar University, Vellore, Tamilnadu, 632 115, India

    M. Syed Ali

  2. Department of Mathematics, Thiruvalluvar University, Vellore, Tamilnadu, 632 115, India

    N. Gunasekaran

  3. Research Center for Wind Energy Systems, Kunsan National University, Kunsan, Chonbuk, 573 701, Korea

    N. Gunasekaran

  4. School of Mathematics, Southeast University, Nanjing, 210096, China

    Jinde Cao  (曹进德)

Authors
  1. M. Syed Ali
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  2. N. Gunasekaran
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  3. Jinde Cao  (曹进德)
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Correspondence to M. Syed Ali.

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Syed Ali, M., Gunasekaran, N. & Cao, J. Sampled-Data State Estimation for Neural Networks with Additive Time–Varying Delays. Acta Math Sci 39, 195–213 (2019). https://doi.org/10.1007/s10473-019-0116-7

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  • DOI: https://doi.org/10.1007/s10473-019-0116-7

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