Asymptotic Stability of Markovian Jumping Genetic Regulatory Networks with Random Delays

This paper investigates the asymptotic stability of genetic regulatory networks with random delays and Markovian jumping parameters. The delay considered here is assumed to be satisfying a certain stochastic characteristic. Corresponding to the probability of the delay taking value in different intervals, stochastic variables satisfying Bernoulli random binary distribution are introduced and a new system model is established by employing the information of the probability distribution. By using a Lyapunov functional approach and linear matrix inequality techniques, the stability criteria for the delayed Markovian jumping genetic regulatory networks are expressed as a set of Linear matrix inequalities (LMIs), which can be solved numerically by LMI toolbox in MATLAB. A genetic network example is given to verify the effectiveness and the applicability of the proposed approach.