A matrix approach to the analysis and computation of robust cycles for Boolean control networks with disturbances

This paper studies several types of robust control cycles (RCCs) for the Boolean control networks (BCNs) affected by disturbances using semi-tensor product of matrices, and provides their computing methods. First, the cycles of a BCN are classified as strong RCCs and weak RCCs according to their ability to resist disturbances. Secondly, the properties of the states on a cycle for the BCNs are revealed, based on which all the RCCs whose weak connecting degree is not more than one with certain length are obtained. Moreover, the controls to ensure that the state trajectories form RCCs are designed. Finally, some examples are given to demonstrate the effectiveness of the obtained theoretical results, as well as to show the applications of these results.