Abstract
In this paper, the problem on asymptotical and robust stability of genetic regulatory networks with time-varying delays and stochastic disturbance is considered. The time-varying delays include not only discrete delays but also distributed delays. The parameter uncertainties are time-varying and norm-bounded. Based on the Lyapunov stability theory and Lur’s system approach, sufficient conditions are given to ensure the stability of genetic regulatory networks. All the stability conditions are given in terms of linear matrix inequalities, which are easy to be verified. Illustrative example is presented to show the effectiveness of the obtained results.
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Acknowledgments
The authors would like to thank the reviewers and the editor for their valuable suggestions and comments which have led to a much improved paper. This work is partially supported by China Postdoctoral Science Foundation (Grant NO. 20060401018), Natural Science Foundation Project of CQ CSCT (Grant NO. 2007BB2395, 2007BB2396).
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Wang, Z., Liao, X., Mao, J. et al. Robust stability of stochastic genetic regulatory networks with discrete and distributed delays. Soft Comput 13, 1199–1208 (2009). https://doi.org/10.1007/s00500-009-0417-1
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DOI: https://doi.org/10.1007/s00500-009-0417-1