Detectability of Delayed Boolean Control Networks Based on Full-Order Observer

This paper investigates the detectability of delayed Boolean control networks (DBCNs) via the Boolean semi-tensor product (BSTP) method. Firstly, three concepts of weak detectability, strong detectability, and detectability for DBCNs are proposed and the dynamics of DBCN are converted into an equivalent algebraic form. Secondly, a full-order observer of DBCNs is constructed to judge the detectabilities of DBCNs by using BSTP. Thirdly, based on the observer, some necessary and sufficient conditions of weak detectability, strong detectability, and detectability for DBCNs are presented. Finally, two examples are illustrated to verify the obtained results.