Partial stability and stabilization of multi-valued logical networks

This paper studies the stability and stabilization of multi-valued logical networks with respect to part of the system's states. By semi-tensor product of matrices, we first convert multi-valued logical networks into a linear discrete-time system. Then a necessary and sufficient condition for partial stability of k-valued logical networks is given. Finally, the stabilization of multi-valued logical control networks by state feedback control is investigated and the corresponding necessary and sufficient condition is obtained. An example is provided to illustrate the efficiency of the obtained results.