Robust exponential stability analysis for stochastic genetic networks with uncertain parameters

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.