Genetic networks play an important role in systems biology as they explain the interactions between genes and proteins. However, the genetic networks are described by dynamical systems with nonlinear uncertainties and usually affected by stochastic internal fluctuations, and stochastic external disturbances. The design addressed in this paper is concerned with robust state estimator of stochastic genetic networks in the presence of nonlinear uncertainties. The objective is to estimate the true concentrations of mRNAs and proteins of the noisy nonlinear genetic networks. Based on the notion of Lyapunov functions, we improve the design condition for the robust estimator to ensure that the estimation error satisfies H_∞ performance criterion. The sufficient condition is derived in terms of parameter-dependent linear matrix inequalities, which are convex constraints, and can be efficiently solved via the sum-of-squares technique. We provide two numerical examples of real genetic networks to illustrate the effectiveness of the proposed method.

Genetic networks play an important role in systems biology as they explain the interactions between genes and proteins. However, the genetic networks are described by dynamical systems with nonlinear uncertainties and usually affected by stochastic internal fluctuations, and stochastic external disturbances. The design addressed in this paper is concerned with robust state estimator of stochastic genetic networks in the presence of nonlinear uncertainties. The objective is to estimate the true concentrations of mRNAs and proteins of the noisy nonlinear genetic networks. Based on the notion of Lyapunov functions, we improve the design condition for the robust estimator to ensure that the estimation error satisfies H_∞绩效标准。充分条件是根据参数相关的线性矩阵不等式导出的，这些不等式是凸约束，可以通过平方和技术有效解决。我们提供了两个真实遗传网络的数值示例，以说明所提出方法的有效性。