Asymptotic stability of probabilistic logical networks with random impulsive effects

This paper investigates the asymptotic set stability of probabilistic logical networks (PLNs) with random impulsive disturbances. A hybrid index model is applied to describe the impulsive PLN. Both the sequence of switching signals and the sequence of impulsive intervals are assumed to be independent and identically distributed (i.i.d.). Some novel methods are proposed to reduce the complexity of calculating invariant subsets and verifying the convergence of homogeneous Markov chains (HMCs). By sampling at impulsive instants, an HMC is obtained from the impulsive PLN, whose initial distribution and transition probability matrix (TPM) are approximately calculated. Based on the obtained HMC, the necessary and sufficient conditions for the asymptotic set stability of the impulsive PLN in hybrid domain and time domain are presented, respectively. Finally, examples are given to illustrate the main results. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper investigates the asymptotic set stability of probabilistic logical networks with random impulsive disturbances, proposing novel methods to reduce complexity. An HMC is obtained by sampling at impulsive instants, leading to necessary conditions for stability of the impulsive network.