Stabilizability analysis of logical networks with switching signal and control input

Abstract This paper mainly investigates the global stability (stabilization) of switched logical (control) networks at one of attractors. Firstly, the switched Boolean (control) networks are transformed into a discrete-time algebraic system by using semi-tensor product (STP) method of matrices. Then, based on this algebraic system, the global stability (stabilization) problem of switched Boolean (control) networks at one of attractors are solved, and the necessary and sufficient conditions are obtained under closed-loop (or open-loop) switching signal and open-loop (or closed-loop) control input, where the open-loop form is given by constructing the digital transformation corresponding to the structure matrix of switched Boolean (control) networks. In addition, similar to the global stability (stabilization) conditions of switched Boolean (control) networks, the relevant conditions for global stability (stabilization) of switched multi-valued logical (control) networks and switched mix-valued logical (control) networks at one of attractors are established. Finally, four examples are given to illustrate the effectiveness of the proposed scheme.