Abstract This paper concerns the detectability problem of Boolean networks with disturbance inputs using the semi-tensor product approach. Detectability like observability describes the ability of the system state to be indirectly measured, which is an important issue to be considered in designing the controller. Four kinds of detectability, weak, weak periodical, strong and strong periodical ones, are defined. A systematic matrix method is developed and formed via three tools respectively called detection operator, detection matrix and detectable set. The former is used to generate the state estimate at each time. The other two are derived from the dynamics of the system and produce several necessary and sufficient conditions for checking detectability. Two examples are provided to demonstrate the effectiveness of the main results. Furthermore, how the proposed methods can be applied and extended to other kinds of disturbance is briefly discussed.

中文翻译：

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具有干扰输入的布尔网络的可检测性

摘要 本文使用半张量积方法研究具有扰动输入的布尔网络的可检测性问题。像可观察性这样的可检测性描述了系统状态被间接测量的能力，这是设计控制器时要考虑的一个重要问题。定义了四种可检测性，弱、弱周期性、强和强周期性。通过分别称为检测算子、检测矩阵和可检测集的三个工具开发和形成系统的矩阵方法。前者用于每次生成状态估计。另外两个来自系统的动力学，并为检查可检测性产生几个必要和充分条件。提供了两个例子来证明主要结果的有效性。此外，