Stabilization of deterministic finite automata based on linear state equation representation

This paper discusses the state feedback stabilization problem of a deterministic finite automaton (DFA), based on its state equation representation recently proposed by the authors. First, a linear state equation representation of the DFA is briefly explained. Next, after the notion of equilibrium points and stabilizability of the DFA are defined, a necessary and sufficient condition for the DFA to be stabilizable is derived. Then under these preparations, a characterization of all stabilizing state feedback controllers is presented. Finally, a simple example is given to show how to follow the proposed procedure.