Stability of stochastic genetic networks with both Markovian jumping parameters and mixed time delays

This paper investigates the issue of stability for stochastic genetic networks with both Markovian jumping parameters and mixed time delays. The jumping parameters are modelled as a continuous-time discrete-state Markovian chain. By constructing Lyapunov functional and using linear matrix inequality (LMI) techniques, sufficient conditions for genetic regulatory networks to be asymptotically stable in the mean square are derived. Two numerical examples are given to illustrate the effectiveness of our results.