New stability conditions for GRNs with neutral delay

Stability Analysis of Genetic Regulatory Networks With General Random Disturbances

This paper establishes the stability criteria for genetic regulatory networks with random disturbances. We assume the nonlinear feedback regulation function to satisfy the sector-like condition and the random perturbation to have a finite second-order moment. First, under the globally Lipschitz condition, the existence and uniqueness of solution to random genetic regulatory networks are considered by exploiting an iterative approximation method. Then, by feat of the random analysis method and matrix technique, sufficient conditions are given to guarantee the noise-to-state stability in mean and globally asymptotic stability in probability, respectively. At last, two simulation examples are exploited in order to verify the validity of the proposed theory.

Kalman Filtering for Genetic Regulatory Networks with Missing Values

The filter problem with missing value for genetic regulation networks (GRNs) is addressed, in which the noises exist in both the state dynamics and measurement equations; furthermore, the correlation between process noise and measurement noise is also taken into consideration. In order to deal with the filter problem, a class of discrete-time GRNs with missing value, noise correlation, and time delays is established. Then a new observation model is proposed to decrease the adverse effect caused by the missing value and to decouple the correlation between process noise and measurement noise in theory. Finally, a Kalman filtering is used to estimate the states of GRNs. Meanwhile, a typical example is provided to verify the effectiveness of the proposed method, and it turns out to be the case that the concentrations of mRNA and protein could be estimated accurately.