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Delay-Probability-Distribution-Dependent Stability of Uncertain Stochastic Genetic Regulatory Networks with Time-Varying Delays

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Abstract

This paper investigates the delay-probability-distribution-dependent stability problem of uncertain stochastic genetic regulatory networks (SGRNs) with time-varying delays. The information of the probability distribution of the time-delay is considered and transformed into parameter matrices of the transferred SGRNs model. Based on the Lyapunov–Krasovskii functional and a stochastic analysis approach, a delay-probability-distribution-dependent sufficient condition is obtained in the linear matrix inequality (LMI) form such that delayed SGRNs are robustly globally asymptotically stable in the mean square for all admissible uncertainties. Three numerical examples are given to illustrate the effectiveness of our theoretical results.

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Acknowledgements

The authors are very much thankful to referees for their valuable comments and suggestions for improving this manuscript.

The work of authors was supported by Department of Science and Technology, New Delhi India under the sanctioned No. SR/S4/MS:485/07.

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Authors and Affiliations

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

    S. Lakshmanan & P. Balasubramaniam

  2. Department of Mathematics, Bharathiar University, Coimbatore, 641 046, Tamilnadu, India

    R. Rakkiyappan

  3. Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603, Kuala Lumpur, Malaysia

    P. Balasubramaniam

Authors
  1. R. Rakkiyappan
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  2. S. Lakshmanan
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  3. P. Balasubramaniam
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Corresponding author

Correspondence to P. Balasubramaniam.

Additional information

P. Balasubramaniam also working as a Visiting Professor, Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia for six months since 12th September 2011.

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Rakkiyappan, R., Lakshmanan, S. & Balasubramaniam, P. Delay-Probability-Distribution-Dependent Stability of Uncertain Stochastic Genetic Regulatory Networks with Time-Varying Delays. Circuits Syst Signal Process 32, 1147–1177 (2013). https://doi.org/10.1007/s00034-013-9595-2

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