On state feedback asymptotical stabilization of probabilistic Boolean control networks

Abstract

This article devotes to the design of all state feedback controllers for the asymptotical stabilization of probabilistic Boolean control networks (PBCNs). Firstly, a class of complete family of reachable sets (CFRSs) is constructed. Based on the CFRSs, all possible state feedback controllers are designed to stabilize PBCNs to a given control-fixed point in distribution. Secondly, by removing the finite-time stabilizers from the controllers that make PBCNs stabilizable in distribution, all state feedback controllers which asymptotically stabilize PBCNs with probability one are further obtained. Thirdly, the CFRSs are applied to solve the problem of asymptotical set stabilization. Finally, an example of lac operon in the Escherichia coli is given to illustrate the proposed methods.