On robust set stability and set stabilization of probabilistic Boolean control networks *

Under the semi-tensor product method, this paper investigates the robust set stability and robust set stabilization problems for a class of probabilistic Boolean control networks (PBCNs) with disturbances. First, an algorithm to determine the largest robust invariant set (LRIS) of a given set for a PBN with probability one is proposed, and the necessary and suf-ficient conditions to detect whether the PBN is globally finite-time stable to this invariant set with probability one are established. Second, the PBNs with control inputs are consid-ered, and an algorithm for the largest robust control invariant set (LRCIS) with probability one is provided, based on which, some necessary and sufficient conditions for finite-time robust set stabilization with probability one of PBCNs are presented. Furthermore, the de-sign scheme of time-optimal state feedback stabilizers via antecedence solution technique is derived. The study of illustrative examples shows the effectiveness of the obtained new results.(c) 2022 Elsevier Inc. All rights reserved.