Stability analysis for continuous-time and discrete-time genetic regulatory networks with delays

This paper investigates the global exponential stability problem for the genetic regulatory networks (GRNs) with delays in both the continuous‐time case and the discrete‐time case. First, Dini derivative method is applied for a new Lyapunov functional to obtain a sufficient condition of the global exponential stability for a class of the continuous‐time GRNs, which is given in the form of several elementary inequalities. This sufficient condition is simple to be easily implemented on the computer. Second, by using the semi‐discretization technique and the IMEX‐θ method, two discrete‐time GRN systems have been derived, which can preserve the dynamical characteristics of the continuous‐time systems. Furthermore, it is shown that under the same sufficient conditions obtained earlier, these two discrete‐time GRN systems are globally exponentially stable. Finally, a pair of examples are given to show the validity of the obtained stability analysis results.