Article

Robust exponential stability analysis for stochastic genetic networks with uncertain parameters

Department of Mathematics, Southeast University, Nanjing 210096, China
Communications in Nonlinear Science and Numerical Simulation DOI:10.1016/j.cnsns.2009.01.004 pp.3369-3378

ABSTRACT In this paper, the robust exponential stability problem is considered for a class of stochastic genetic networks with uncertain parameters. Under assumptions that the parameter uncertainties are norm bounded, both cases that the genetic network has or has not time delays are discussed. Sufficient conditions are derived to guarantee the robust exponential stability in the mean square of stochastic genetic networks for all admissible parameter uncertainties. By applying Lyapunov function (functional) and conducting some stochastic analysis, the stability criteria are given in the form of linear matrix inequalities (LMI’s), which can be easily checked in practice. Two illustrative examples are also given to show the usefulness of the proposed criteria.

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    Article: On robust stability of stochastic genetic regulatory networks with time delays: a delay fractioning approach.
    Yao Wang, Zidong Wang, Jinling Liang
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    ABSTRACT: 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 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.
    IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics: a publication of the IEEE Systems, Man, and Cybernetics Society 10/2009; 40(3):729-40. · 3.01 Impact Factor
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Keywords

admissible parameter uncertainties
 
applying Lyapunov function
 
cases
 
linear matrix inequalities
 
parameter uncertainties
 
proposed criteria
 
robust exponential stability
 
robust exponential stability problem
 
stochastic genetic networks
 
time delays
 
uncertain parameters
 

Guanjun Wang