Gene networks in biological systems are highly complicated because of their nonlinear and stochastic features. Network dynamics typically involve crosstalk mechanism and they may suffer from corruption due to intrinsic and extrinsic stochastic molecular noises. Filtering noises in gene networks using biological techniques accompanied with a systematic strategy is thus an attractive topic. However, most states of biological systems are not directly accessible. In practice, these immeasurable states can only be predicted based on the measurement output. In the lab experiment, green fluorescent protein (GFP) is commonly adopted as the reporter protein since it is able to reflect intensity of the gene expression. On this basis, this study considers a nonlinear stochastic model to describe the stochastic gene networks and shows that robust state estimation using Kalman filtering techniques is possible. Stability of the robust estimation scheme is analyzed based on the Ito’s theorem and Lyapunov stability theory. Numerical examples in silico are illustrated to confirm performance of the proposed design.
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