Stability Criteria for Genetic Regulatory Networks with Time Delays

This paper aims at proposing a new method to establish stability criteria for a class of genetic regulatory networks with time delays. By using the property of calculus and the Lagrange's Mean-Value Theorem to reduce the order of system model, we get a reduced-order system with distributed delays and bounded uncertain parameters, which simplifies the problem under consideration. By the help of Hospital's rule and the definition of stability, the relationship between stability for the reduced-order model and the original one is obtained. Based on the Lyapunov stability theory, Cauchy-Schwarz inequality, linear matrix inequalities and convex combination technique, the robust asymptotic stability criterion of the reduced-order system are established. From which, the asymptotic stability criterion for the original system is derived. The simulation results of a numerical example show the validity of the proposed approach.