Stability and Stabilization of Boolean Networks with Stochastic Delays

In this paper, stability and stabilization of Boolean networks with stochastic delays are studied via semi-tensor product of matrices. The stochastic delays, randomly attaining finite values, are modeled by Markov chains. By utilizing an augmented method, the considered Boolean network is first converted into two coupled Markovian switching systems without delays. Then, some stochastic stability results are obtained based on stability results of positive systems. Subsequently, the stabilization of Boolean networks with stochastic delays is further investigated, and an equivalent condition for the existence of feedback controllers is provided in terms of a convex programming problem, which can be easily solved and also conveniently applied to design controller gains. Finally, numerical examples are given to illustrate feasibility of the obtained results.