Stabilization of Impulsive BNs With Stochastic Disturbances: An Aperiodic/Periodic Scheme

Abstract

This brief investigates the stabilization problem for impulsive Boolean networks (BNs) with stochastic disturbances. Firstly, dynamic evolution of the impulsive BN is converted into an algebraic form by using the semi-tensor product method of matrices. By analyzing the reachable set, the notion of distance between each state of the network and the equilibrium is defined, based on which the algorithm is then proposed for designing the appropriate aperiodic impulsive sequences. After that, based on the state-feedback control method, some criteria are presented to stabilize the Boolean control networks with periodic impulses and stochastic disturbances. Numerical examples are also presented to show feasibility of the theoretical results established.