Distributed pinning controllers design for set stabilization of $k$-valued logical control networks

Design of distributed pinning controllers for set stabilization of $k$-valued logical control networks is investigated in this paper. Firstly, by analyzing the coupling correlations among nodes, pinned node set is determined. Secondly, based on the solvability of a class of matrix equations, sufficient conditions which resort to local information are put forward for the design of pinning controllers. Furthermore, an algorithm for designing pinning feedback controllers is presented, where the designed controllers are related to part of state variables instead of all variables. Finally, two illustrative examples are presented to verify the effectiveness of the main results.