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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.

Stability analysis of multi-valued logical networks with Markov jump disturbances