Delay-dependent asymptotic stability criteria for genetic regulatory networks with impulsive perturbations

This paper considers the problem for asymptotic stability of genetic regulatory networks with impulse control using the delay partitioning approach. By using the direct Lyapunov method, a new Lyapunov-Krasovskii functional is introduced based on the decomposition approach. Time delays here are assumed to be time-varying and belong to the given intervals. When dealing with the time derivative of Lyapunov functional, a new tight integral inequality is adopted for bounding the cross terms. Then, a new less conservative delay-dependent stability criterion is formulated in terms of linear matrix inequalities (LMIs), which can be easily solved by the Matlab LMI toolbox. Finally, the proposed method is validated through the numerical simulation, which shows the effectiveness of the presented stability criteria.