Pinning detectability of Boolean control networks with injection mode

<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 current state system according known input-output sequences. Using Cheng product matrices, BNPCIM can be converted into a special algebraic form BCNs mix-valued logical control. Based different research requirements, three types for are proposed: weak detectability, strong detectability. Under free networked input conditions, sequence matrices constructed reflect output information by explicit forms. Then using established several necessary sufficient conditions derived. Moreover, avoid unnecessary calculations, maximum steps achieve gained. Finally, two illustrative examples given demonstrate effectiveness obtained results.</p>