On robust control invariance of Boolean control networks

This paper investigates the robust control invariance of Boolean control networks (BCNs) via the semi-tensor product of matrices. Firstly, based on an algebraic state space representation of BCNs, two necessary and sufficient conditions are presented to check whether or not a given set is a robust control invariant set under a given state feedback controller. Secondly, by defining a series of suitable sets, all possible state feedback gain matrices under which a given set is a robust control invariant set are characterized. An illustrative example is presented to demonstrate the obtained new results.