Robust Stability of Stochastic Genetic Regulatory Networks with Time-Varying Delays

In this paper, the global robust asymptotical stability of delayed genetic regulatory networks with stochastic disturbance and SUM regulatory functions is studied. Time delays are assumed to be time-varying and differentiable, the parameter uncertainties are time-varying and norm-bounded. Based on the Lypapunov method and Lur'e system approach, sufficient conditions are given to ensure the stability of the genetic regulatory networks. All the stability conditions are given in terms of LMIs which are easy to be verified. Illustrative example is presented to show the effectiveness of the obtained results.

[1]  D. A. Baxter,et al.  Mathematical Modeling of Gene Networks , 2000, Neuron.

[2]  L. Serrano,et al.  Engineering stability in gene networks by autoregulation , 2000, Nature.

[3]  Xuyang Lou,et al.  On the global robust asymptotic stability of BAM neural networks with time-varying delays , 2006, Neurocomputing.

[4]  K. Aihara,et al.  Synchronization of coupled nonidentical genetic oscillators , 2006, Physical biology.

[5]  Ruiqi Wang,et al.  Modelling periodic oscillation of biological systems with multiple timescale networks. , 2004, Systems biology.

[6]  Jinde Cao,et al.  Asymptotic and robust stability of genetic regulatory networks with time-varying delays , 2008, Neurocomputing.

[7]  K. Aihara,et al.  Stability of genetic regulatory networks with time delay , 2002 .

[8]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[9]  Kevin Burrage,et al.  Stochastic approaches for modelling in vivo reactions , 2004, Comput. Biol. Chem..

[10]  Kazuyuki Aihara,et al.  Stability of Genetic Networks With SUM Regulatory Logic: Lur'e System and LMI Approach , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  E. Davidson,et al.  Genomic cis-regulatory logic: experimental and computational analysis of a sea urchin gene. , 1998, Science.

[12]  Farren J. Isaacs,et al.  Computational studies of gene regulatory networks: in numero molecular biology , 2001, Nature Reviews Genetics.

[13]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[14]  Hidde de Jong,et al.  Modeling and Simulation of Genetic Regulatory Systems: A Literature Review , 2002, J. Comput. Biol..

[15]  P. Shi,et al.  Novel robust stability criteria for uncertain stochastic Hopfield neural networks with time-varying delays , 2007 .

[16]  M. Elowitz,et al.  A synthetic oscillatory network of transcriptional regulators , 2000, Nature.

[17]  Guanrong Chen,et al.  LMI-based approach for asymptotically stability analysis of delayed neural networks , 2002 .

[18]  Xiaofeng Liao,et al.  Corrections to "LMI-based Approach for Asymptotically Stability Analysis of Delayed Neural Networks" , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..