Robust set stability of probabilistic Boolean networks under general stochastic function perturbation

Abstract

This paper concentrates on the impact of stochastic function perturbation (SFP) on the set stability of PBNs. The problem of robust set stability is divided into two cases, and they are respectively the perturbed column of the structure matrix does not belong to/belongs to the stabilizing set. For the first case, two necessary and sufficient conditions are obtained to guarantee that the system can keep finite-time stable unchanged and the system becomes asymptotically stable, respectively. For the second case, i.e., the perturbed column in the stabilizing set, the condition which can keep the stability of the system unchanged is obtained. Lastly, an example is provided to illustrate the obtained theoretical results.