Pinning control design for state feedback stabilization of multi-valued logical control networks

This paper investigates the state feedback stabilization of multi-valued logical control networks via the semi-tensor product of matrices. Firstly, based on an algebraic representation of multi-valued logical control networks, a necessary and sufficient condition is presented for the pinning control design of state feedback stabilization of multi-valued logical control networks. Secondly, under the situation of state and input constraints, a necessary and sufficient condition is presented for the constrained state feedback pinning control design. Two illustrative examples are worked out to illustrate the proposed design procedure.