I-detectability is an important issue in partially observed discrete event systems (DESs). In this paper, a Boolean semi-tensor product (BSTP) approach is proposed to investigate the I-detectability problem of partially observed DESs. First, two concepts of I-detectability, that is, strong I-detectability and weak I-detectability, are recalled for partially observed DESs. Second, in order to estimate the initial state of DESs after finite observation events, an observer is constructed and converted to an algebraic form based on BSTP. Third, based on the algebraic form of observer, two necessary and sufficient conditions are presented for strong I-detectability and weak I-detectability of partially observed DESs, respectively. Finally, two examples are given to illustrate the obtained results.

中文翻译：

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部分观察到的离散事件系统的 I 可检测性的矩阵方法

I-可检测性是部分观测离散事件系统 (DES) 中的一个重要问题。在本文中，提出了一种布尔半张量积（BSTP）方法来研究部分观察到的 DES 的 I 可检测性问题。首先，对于部分观察到的 DES，回忆了两个 I-可检测性概念，即强 I-可检测性和弱 I-可检测性。其次，为了估计 DES 在有限观测事件后的初始状态，构造了一个观测器并将其转换为基于 BSTP 的代数形式。第三，基于观察者的代数形式，分别给出了部分观测到的DES的强I-可检测性和弱I-可检测性的两个充分必要条件。最后，给出两个例子来说明得到的结果。