Research On A Boolean Network With Impulsive Disturbance

As an important branch of logic dynamical system,Boolean network(BN)has been widely used to simulate gene regulatory network(GRN).In the past decade,the research and analysis on impulsive BNs have made significant progress,such as stability,stabilization,controllability,observability,synchronization and so on.However,the research object is mainly BNs with time-triggered impulses,and there are still many problems to be solved about BNs with statetriggered impulses.Based on this,this article investigates the set stabilization and asymptotical feedback controllability(AFC)of state-triggered random impulsive Boolean control networks(SRIBCNs).The main results of this paper are as follows:Based on the semi-tensor product of matrices,the state-feedback stabilization problem of SRIBCNs is studied by utilizing a hybrid index model.Firstly,four kinds of definitions of stabilizability are proposed for SRIBCNs.In order to avoid Zeno phenomenon,we give the concept of forward completeness and further derive a necessary and sufficient condition for the forward completeness of SRIBCNs.Based on the properties of the largest control invariant subset,the necessary and sufficient condition for the finite-time feedback stabilization of SRIBCNs is derived.On this basis,the necessary and sufficient condition for the asymptotic case is also obtained,and the state-feedback stabilizers are constructed by layering the state space.The relationships between different stabilizabilities are also compared.Based on the study regarding feedback stabilization and the properties of the largest invariant subset,a necessary and sufficient condition for the asymptotical feedback reachability(AFR)between two states of SRIBCN is derived.By introducing the reachability matrix,the necessary and sufficient conditions for the AFR of the specific state and the AFC of SRIBCN are obtained.Finally,the relationship between AFC and other controllability is discussed with examples.