Stability analysis is the most basic and important problem of dynamic systems, which has been extensively studied in the last few decades. The research on finite-time stability and stability in distribution of k-valued logical networks (KVLNs) with Markov jump disturbances (MJDs) is considered in this paper. To begin with, we establish an equivalent Markov jump system for the considered KVLNs with MJDs via semi-tensor product (STP) of matrices, which can simplify the stability analysis of KVLNs with MJDs. Next, two criteria are proposed for finite-time stability and stability in distribution of KVLNs with MJDs, respectively. At last, the validity of the obtained results is illustrated by simulation on the apoptosis network.

稳定性分析是动力系统最基本和最重要的问题，在过去的几十年里得到了广泛的研究。本文研究了具有马尔可夫跳跃扰动(MJDs)的k值逻辑网络(KVLNs)分布的有限时间稳定性和稳定性。首先，我们通过矩阵的半张量积（STP）为所考虑的具有 MJD 的 KVLN 建立了一个等效的马尔可夫跳跃系统，这可以简化具有 MJD 的 KVLN 的稳定性分析。接下来，分别针对具有 MJD 的 KVLN 分布的有限时间稳定性和稳定性提出了两个标准。最后通过细胞凋亡网络仿真验证了所得结果的有效性。