On Robust Stability of Stochastic Genetic Regulatory Networks With Time Delays: A Delay Fractioning Approach

Yao Wang, Zidong Wang, Jinling Liang
2010 IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)  
Robust stability serves as an important regulation mechanism in system biology and synthetic biology. In this paper, the robust stability analysis problem is investigated for a class of nonlinear delayed genetic regulatory networks with parameter uncertainties and stochastic perturbations. The nonlinear function describing the feedback regulation satisfies the sector condition, the time delays exist in both translation and feedback regulation processes, and the state-dependent Brownian motions
more » ... t Brownian motions are introduced to reflect the inherent intrinsic and extrinsic noise perturbations. The purpose of the addressed stability analysis problem is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. By utilizing a new Lyapunov functional based on the idea of "delay fractioning", we employ the linear matrix inequality (LMI) technique to derive delay-dependent sufficient conditions ensuring the robust stability of the gene regulatory networks. Note that the obtained results are formulated in terms of LMIs that can easily be solved using standard software packages. Simulation examples are exploited to illustrate the effectiveness of the proposed design procedures. Index Terms-Genetic regulatory networks (GRNs), linear matrix inequality (LMI), Lyapunov-Krasovskii functional, robust stability, stochastic perturbation, time delays, uncertain system.
doi:10.1109/tsmcb.2009.2026059 pmid:19884095 fatcat:gmfz5f66zja3zmb4fsp3qiaojm