Sampled-data stabilization of probabilistic Boolean control networks

Abstract

Probabilistic Boolean networks (PBNs) are discrete-time systems composed of a family of Boolean networks (BNs), between which the PBN switches in a stochastic fashion. In this paper, we address the stabilization of probabilistic Boolean control networks (PBCNs) via a sampled-data state feedback controller (SDSFC). Based on the algebraic representation of logical functions, a necessary and sufficient condition is derived for the existence of SDSFCs for the global stabilization of PBCNs, and the controller is further designed. A biological example is presented to illustrate the effectiveness of the obtained results.