Controllability of Markovian jump Boolean control networks

In this paper, controllability of Markovian jump Boolean control networks (MJBCNs) is studied via semi-tensor product of matrices. First, based on the algebraic expression of the considered Boolean control networks, a necessary and sufficient condition for controllability is presented by iteration equations, which however may lead to high-dimensional matrices. To avoid having such matrices, a new matrix is defined and applied to derive another equivalent condition to verify controllability of MJBCNs. Moreover, a maximum principle of MJBCNs is established to further study the minimal controllable time. Finally, two examples are presented to illustrate the obtained results.Ministry of Education (MOE)Accepted versionThe work was partially supported by Ministry of Education, Singapore,under contract of MOE2016-T2-1-119. The material in this paper was notpresented at any conference. This paper was recommended for publication inrevised form by Associate Editor Jamal Daafouz under the direction of EditorRichard Middleton.