State feedback stabilization of generic logic systems via Ledley antecedence solution

In this paper, the application of Ledley antecedence solutions in designing state feedback stabilizers of generic logic systems has been proposed. To make the method feasible, two modifications are made to the original Ledley antecedence solution theory: (i) the preassigned logical functions have been extended from being a set of equations to an admissible set; (ii) the domain of arguments has been extended from the whole state space to a restricted subset. In the proposed method, state feedback controls are considered as a set of extended Ledley antecedence solutions for a designed iterative admissible sets over their corresponding restricted subsets. Based on this, an algorithm has been proposed to verify the solvability and simultaneously provide all possible time‐optimal state feedback stabilizers when the problem is solvable. Demonstrations of the proposed method on both the Boolean control networks and mix‐valued logical systems have validated the effectiveness of the proposed method in stabilizing logic systems in general.