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.

本文研究了切换信号满足预先指定最小驻留时间约束的切换布尔网络（switched Boolean networks, SBNs）的稳定性问题。首先，采用半张量积方法建立了带最小驻留时间的切换布尔网络的代数状态空间表示。其次，针对两类情形研究该类切换布尔网络的全局稳定性：(i) 各子系统的最小驻留时间相同；(ii) 各子系统的最小驻留时间不同。通过构造若干具有任意切换信号的切换布尔网络，给出了若干判定带最小驻留时间的切换布尔网络稳定性的充要条件。此外，针对子系统平衡点各不相同的情形，提出了一种设计状态依赖切换信号的方法，使得带最小驻留时间的切换布尔网络能够局部稳定于期望平衡点。最后，通过两个算例验证了所得结果的有效性。