Stochastic Stability of Genetic Regulatory Networks with Mixed Delays
Zhengxia Wang, Guodong Liu, Darong Huang and Jun Song
Affiliation: Department of Computer Science and Engineering, Chongqing Jiaotong University, Chongqing 400044, China.
In this paper, the asymptotical stability of stochastic genetic regulatory networks with time-varying delays and
continuous distributed delays are investigated. The constraint that derivative of time-varying delays must be smaller than
1 is relaxed, and the activation functions are of more general descriptions, which generalize and improve the earlier methods.
Based on the Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI) techniques defined on
convex set, stability criteria for stochastic delayed genetic regulatory networks are established in the form of LMIs, which
can be easily verified. Numerical example is also given to demonstrate the effectiveness of the proposed criteria.
Keywords: Distributed delays, Genetic regulatory network, Linear matrix inequality (LMI), Stochastic system, Time-varying delays.
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