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Robust stability of stochastic genetic regulatory networks with time-varying delays: a delay fractioning approach

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Abstract

This paper is concerned with the problem of the globally asymptotically mean square stability for a class of delayed genetic regularity networks (GRNs) with both parameter uncertainties and stochastic disturbances, where the time delays are belong to given intervals and assumed to be time varying. Based on choosing an appropriate and novel Lyapunov functional, a “delay fractioning” approach that is different from the existing ones is introduced. By utilizing \(It\hat{o}\hbox{'}s\) differential formula and using the linear matrix inequality (LMI) method, we derive a robust asymptotical stability criterion in mean square sense for uncertain GRNs with time-varying delays. All the stability conditions are given in terms of LMIs. One example and its simulation are provided to show the advantages of the obtained result.

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Acknowledgments

This work is partially supported by the fund Heilongjiang Education Committee under Grant No. 12521429, the fund of Heilongjiang University Innovation Team Support Plan under Grant No. Hdtd2010–03 and the fund of Heilongjiang University Student Academic and Technological Innovation Projects. The authors thank the anonymous referees for their helpful comments and suggestions that improve greatly this note.

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Authors and Affiliations

  1. School of Mathematical Science, Heilongjiang University, Harbin, 150080, China

    Yantao Wang, Ahui Yu & Xian Zhang

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  1. Yantao Wang
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  2. Ahui Yu
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  3. Xian Zhang
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Correspondence to Xian Zhang.

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Wang, Y., Yu, A. & Zhang, X. Robust stability of stochastic genetic regulatory networks with time-varying delays: a delay fractioning approach. Neural Comput & Applic 23, 1217–1227 (2013). https://doi.org/10.1007/s00521-012-1034-y

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  • DOI: https://doi.org/10.1007/s00521-012-1034-y

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