Abstract：
This study discusses the robust stability problem of Boolean networks (BNs) with data loss and disturbances, where data loss is appropriately described by random Bernoulli distribution sequences. Firstly, a BN with data loss and disturbances is converted into an algebraic form via the semi-tensor product (STP) technique. Accordingly, the original system is constructed as a probabilistic augmented system, based on which the problem of stability with probability one for the original system becomes a set stability with probability one for the augmented system. Subsequently, certain criteria are proposed for the robust stability of the systems. Moreover, an algorithm is developed to verify the robust set stability of the augmented system based on truth matrices. Finally, the validity of the obtained results is demonstrated by an illustrative example.
摘要：
本研究讨论了具有数据丢失和干扰的布尔网络(BNs)的鲁棒稳定性问题,其中数据丢失由随机伯努利分布序列适当地描述。首先,通过半张量积（STP）技术将具有数据丢失和干扰的BN转换为代数形式。因此，原始系统被构造为概率增强系统，基于此，原始系统的概率为1的稳定性问题成为增广系统的概率为1的集合稳定性。随后，提出了系统鲁棒稳定性的若干准则。此外，提出了一种基于真值矩阵的增广系统的鲁棒集稳定性验证算法。最后,通过一个说明性的例子证明了所得结果的有效性。
