Constrained Sampled-Data Reachability and Stabilization of Logical Control Networks

This brief investigates the sampled-data reachability and stabilization of k-valued logical control networks (KVLCNs) with state and input constraints. First, using the semi-tensor product of matrices, the equivalent algebraic forms of KVLCNs and sampled-data control are obtained. Second, a kind of constrained sampled-data controllability matrix is constructed by using the algebraic form, based on which, a necessary and sufficient condition is presented for the constrained sampled-data reachability of KVLCNs. Third, a necessary and sufficient condition is proposed for the constrained sampled-data stabilization of KVLCNs by defining a series of sampled-data reachable sets. Finally, an example is given to illustrate the effectiveness of the obtained results.