Static output feedback stabilization of deterministic finite automata

In this paper, we investigate the static output feedback stabilization (SOFS) of deterministic finite automata (DFA) by using semi-tensor product (STP) theory. Firstly, the matrix expression of Moore-type automata with states, inputs and outputs is presented by using the algebraic equations. The feasible events matrix (FEM) is given in the matrix form by using STP theory and the transition-state adjacency matrix of DFA is presented through Boolean operation. Secondly, the concept of prereachability set and some corresponding properties are introduced, and then we obtain the necessary and sufficient conditions about the SOFS. In the end, an example is presented to illustrate the effectiveness of the results.