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Robust state estimation for discrete-time genetic regulatory networks with randomly occurring uncertainties

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Abstract

In this paper, we investigate the problem of robust state estimator design for a class of uncertain discrete-time genetic regulatory networks (GRNs) with time varying delays and randomly occurring uncertainties. By introducing a new discretized Lyapunov–Krasovskii functional together with a free-weighting matrix technique, first we derive a set of sufficient conditions for the existence of global asymptotic state estimator for the discrete-time GRN model with time delays satisfying both the lower and the upper bound of the interval time-varying delay. Further, the obtained results are extended to deal the robust state estimator design for the discrete-time GRN model in the presence of randomly occurring uncertainties which obey certain mutually uncorrelated Bernoulli distributed white noise sequences. The proposed criterions are established in terms of linear matrix inequalities (LMIs) which can be easily solved via Matlab LMI toolbox. Finally, the robust state estimator design has been implemented in a gene network model to illustrate the applicability and usefulness of the obtained theory.

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Acknowledgements

The work of J.H. Park was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2013R1A1A2A10005201).

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Authors and Affiliations

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

    R. Sakthivel

  2. Department of Mathematics, Anna University—Regional Centre, Coimbatore, 641 047, India

    K. Mathiyalagan

  3. Department of Electrical Engineering/Information and Communication Engineering, Yeungnam University, Dae-dong, Kyongsan, 712-749, Republic of Korea

    Ju H. Park

  4. Department of Mathematics, Faculty of Science, UAE University, Al-Ain, 15551, UAE

    S. Lakshmanan

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  1. R. Sakthivel
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  2. K. Mathiyalagan
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  3. S. Lakshmanan
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  4. Ju H. Park
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Corresponding authors

Correspondence to K. Mathiyalagan or Ju H. Park.

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Sakthivel, R., Mathiyalagan, K., Lakshmanan, S. et al. Robust state estimation for discrete-time genetic regulatory networks with randomly occurring uncertainties. Nonlinear Dyn 74, 1297–1315 (2013). https://doi.org/10.1007/s11071-013-1041-2

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  • DOI: https://doi.org/10.1007/s11071-013-1041-2

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