In this paper, the controllability and observability of sampled-data Boolean control networks (SDBCNs) are investigated. New phenomena are observed in the study of the controllability and observability of SDBCNs. We routinely convert SDBCNs into linear discrete-time systems by the semitensor product of matrices. Necessary and sufficient conditions are derived for the controllability of SDBCNs. After that, we combine two SDBCNs with the same transition matrix into a new SDBCN to study the observability. Using an iterative algorithm, a stable row vector ${\mathcal {U}}^*$, called the observability row vector, in finite iterations, is obtained. It is proved that an SDBCN is observable, if and only if $\Vert {\mathcal {U}}^*\Vert _1=N^2-N$ with $N:=2^n$, where $n$ is the number of state-variables of BNs. Moreover, based on graph theory, a more effective algorithm is given to determine the observability of SDBCNs. Its complexity is not related to the length of the sampling period. In addition, some equivalent necessary and sufficient conditions are put forward for the observability of SDBCNs. Numerical examples are given to demonstrate the effectiveness of the obtained results.

中文翻译：

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通过采样数据控制布尔控制网络的可控性和可观察性

本文研究了采样数据布尔控制网络（SDBCN）的可控性和可观察性。在研究SDBCNs的可控性和可观察性中观察到了新现象。我们通常通过矩阵的半张量积将SDBCN转换为线性离散时间系统。得出了SDBCN的可控性的必要条件和充分条件。之后，我们将具有相同过渡矩阵的两个SDBCN合并到一个新的SDBCN中，以研究可观察性。使用迭代算法，稳定的行向量$ {\数学{U}} ^ * $在有限的迭代中，获得了称为可观察性的行向量。证明了SDBCN是可观察的，当且仅当$ \ Vert {\ mathcal {U}} ^ * \ Vert _1 = N ^ 2-N $ 和 $ N：= 2 ^ n $， 在哪里 $ n $是BN的状态变量的数量。此外，基于图论，给出了一种更有效的算法来确定SDBCN的可观察性。它的复杂性与采样周期的长度无关。此外，还为SDBCN的可观测性提出了一些等效的必要条件和充分条件。数值例子说明了所获得结果的有效性。