Robust stochastic stability analysis of Markovian switching genetic regulatory networks with discrete and distributed delays

In this paper, we investigate robust stochastic stability of Markovian switching genetic regulatory networks with discrete and distributed delays. Different from previous correspondingly works, discrete and distributed delays are involved to describe the concentration of macromolecule for genetic networks. Based on the Lyapunov stability theory and linear matrix inequality (LMI), sufficient conditions are given to ensure the stability in the mean square of the stochastic genetic networks with Markovian switching. An illustrative example is given to show the effectiveness of our theoretical results.

[1]  Kazuyuki Aihara,et al.  Multivariate analysis of noise in genetic regulatory networks. , 2004, Journal of theoretical biology.

[2]  Jinde Cao,et al.  Exponential Stability of Discrete-Time Genetic Regulatory Networks With Delays , 2008, IEEE Transactions on Neural Networks.

[3]  Long-Yeu Chung,et al.  Global asymptotic stability for cellular neural networks with discrete and distributed time-varying delays , 2007 .

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

[5]  Jinde Cao,et al.  Global asymptotic and robust stability of recurrent neural networks with time delays , 2005, IEEE Trans. Circuits Syst. I Regul. Pap..

[6]  K. Burrage,et al.  Stochastic delay differential equations for genetic regulatory networks , 2007 .

[7]  Jun Hu,et al.  Robust stability of genetic regulatory networks with interval time-varying delays under intrinsic and extrinsic noises , 2010, Proceedings of the 29th Chinese Control Conference.

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

[9]  Yurong Liu,et al.  Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays , 2006 .

[10]  Zidong Wang,et al.  Robust stability analysis of generalized neural networks with discrete and distributed time delays , 2006 .

[11]  T. Chu,et al.  LMI conditions for stability of neural networks with distributed delays , 2007 .

[12]  E. Sánchez,et al.  Input-to-state stability (ISS) analysis for dynamic neural networks , 1999 .

[13]  Jianhua Sun,et al.  Exponential stability of reaction–diffusion generalized Cohen–Grossberg neural networks with time-varying delays , 2007 .

[14]  Bing Chen,et al.  Mean square exponential stability of stochastic fuzzy Hopfield neural networks with discrete and distributed time-varying delays , 2009, Neurocomputing.

[15]  Jinde Cao,et al.  Robust exponential stability analysis for stochastic genetic networks with uncertain parameters , 2009 .

[16]  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.

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

[18]  Jinde Cao,et al.  New conditions for global exponential stability of cellular neural networks with delays , 2005, Neural Networks.

[19]  Yonghui Sun,et al.  Stochastic stability of Markovian switching genetic regulatory networks , 2009 .

[20]  X. Mao,et al.  Robust stability of uncertain stochastic differential delay equations , 1998 .

[21]  Jinde Cao,et al.  Robust stability of genetic regulatory networks with distributed delay , 2008, Cognitive Neurodynamics.

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