Stability analysis for switched Boolean networks with minimum dwell time

This paper investigates the stability of switched Boolean networks (SBNs) whose switching signal obeys a pre-specified minimum dwell time constraint. Firstly, the algebraic state space representation of the SBN with minimum dwell time is established using the semi-tensor product method. Secondly, the global stability of these kinds of SBNs is investigated by two cases: (i) the minimum dwell time of each subsystem is the same; (ii) the minimum dwell time of each subsystem is different. By constructing some SBNs with arbitrary switching signal, several necessary and sufficient conditions are provided to detect the stability of the SBN with minimum dwell time. Moreover, for the case that subsystems have different equilibrium points, a method to design the state-dependent switching signals is proposed such that the SBN with minimum dwell time can be locally stable to a desired equilibrium point. Finally, two examples are proposed to demonstrate the effectiveness of the results.