Controllability analysis of multi-valued logical control networks

The controllability of multi-valued logical control networks is discussed in this paper. Using the vector form of multi-valued logical variable, the multi-valued logical control network is expressed as a bilinear discrete time system about the state and control variables. Based on the algebraic form, two definitions of controllability avoiding undesirable states set C are introduced: One is for the general controllability avoiding C, and the other one is for s fixed times controllability avoiding C. Also two necessary and sufficient conditions are given for each case.