The Robustness of Outputs With Respect to Disturbances for Boolean Control Networks

In this brief, we investigate the robustness of outputs with respect to disturbances for Boolean control networks (BCNs) by semi-tensor product (STP) of matrices. First, BCNs are converted into the corresponding algebraic forms by STP, then two sufficient conditions for the robustness are derived. Moreover, the corresponding permutation system and permutation graph are constructed. It is proven that if there exist controllers such that the outputs of permutation systems are robust with respect to disturbances, then there must also exist controllers such that the outputs of the corresponding original systems achieve robustness with respect to disturbances. One effective method is proposed to construct controllers to achieve robustness. Examples are also provided to illustrate the correctness of the obtained results.