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.

中文翻译：

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具有开关信号和控制输入的逻辑网络的稳定性分析

摘要 本文主要研究切换逻辑（控制）网络在一个吸引子上的全局稳定性（stabilization）。首先，使用矩阵的半张量积（STP）方法将切换后的布尔（控制）网络转化为离散时间代数系统。然后，基于该代数系统，求解其中一个吸引子的开关布尔（控制）网络的全局稳定性（稳定）问题，得到闭环（或开环）开关信号下的充要条件和开环（或闭环）控制输入，其中开环形式是通过构造对应于开关布尔（控制）网络结构矩阵的数字变换给出的。此外，类似于切换布尔（控制）网络的全局稳定性（稳定）条件，切换多值逻辑（控制）网络和切换混合值逻辑（控制）网络在一个吸引子处的全局稳定性（稳定）相关条件成立。最后，给出了四个例子来说明所提出方案的有效性。