Stochastic stability of Markovian switching genetic regulatory networks

In this Letter, taking into account the structure variations at discrete time instances during the process of gene regulation, a hybrid genetic regulatory networks model based on Markov chain is proposed. Its robust stochastic stability in the case of uncertain switching probabilities and intrinsic noises is then addressed from the stochastic system point of view. It is shown that the sufficient condition for the robust stochastic stability of the genetic networks can be formulated as feasibility of a linear matrix inequality, which can be easily facilitated by Matlab LMI toolbox. Finally, a numerical example with simulations is presented to illustrate the effectiveness of the developed results.