Pinning detectability of Boolean control networks with injection mode

Abstract

<p style='text-indent:20px;'>This technical note presents analytical investigations on detectability of Boolean network with pinning control and injection mode (BNPCIM). Detectability represents the property to uniquely determine the current state of the system according to known input-output sequences. Using Cheng product of matrices, BNPCIM can be converted into a special algebraic form of BCNs with mix-valued logical control. Based on different research requirements, three types of detectability for BNPCIM are proposed: weak detectability, detectability and strong detectability. Under free and networked input conditions, a sequence of matrices are constructed to reflect output and state information by explicit forms. Then by using the established matrices, several necessary and sufficient conditions for three types of detectability are derived. Moreover, to avoid unnecessary calculations, the maximum steps to achieve different detectability are gained. Finally, two illustrative examples are given to demonstrate the effectiveness of the obtained results.</p>