On the Transient and Steady-State Estimates of Interval Genetic Regulatory Networks

This paper is concerned with the transient and steady-state estimates of a class of genetic regulatory networks (GRNs). Some sufficient conditions, which do not only present the transient estimate but also provide the estimates of decay rate and decay coefficient of the GRN with interval parameter uncertainties (interval GRN), are established by means of linear matrix inequality (LMI) and Lyapunov-Krasovskii functional. Moreover, the steady-state estimate of the proposed GRN model is also investigated. Furthermore, it is well known that gene regulation is an intrinsically noisy process due to intracellular and extracellular noise perturbations and environmental fluctuations. Then, by utilizing stochastic differential equation theory, the obtained results are extended to the case with noise perturbations due to natural random fluctuations. All the conditions are expressed within the framework of LMIs, which can easily be computed by using standard numerical software. A three-gene network is provided to illustrate the effectiveness of the theoretical results.