Controllability and set controllability of periodically switched Boolean control networks

Abstract

This paper investigates the controllability and set controllability of periodically switched Boolean control networks (PSBCNs) via the semi-tensor product. Firstly, the algebraic form of switching signal is given and a parallel system is formed by combining the switching signal and the state. Then the controllability problem of PSBCNs is transformed into the set controllability problem of the new system, further, the criterion for controllability is obtained. Secondly, the set controllability matrix of PSBCNs is constructed, and the necessary and sufficient condition of set controllability for PSBCNs is presented. In addition, a more general PSBCN is considered and the criteria for its controllability and set controllability are proposed. Finally, a practical example is given to illustrate the obtained results, which shows that our new results are correct and effective.