On the stabilization of nondeterministic finite automata via static output feedback.

A nondeterministic finite automaton (NDFA) can exhibit an uncertain behavior in modeling and analysis, and its stabilization is viewed as an essential component of theoretical research. In this paper, we focused on the problem of static output feedback stabilization of NDFA under the framework of matrix semi-tensor product (matrix STP). First, the dynamics of Moore-type NDFA can be described as a discrete-time bilinear expression by a matrix-based modeling approach. Subsequently, equilibrium point and closed transition matrix of NDFA are introduced, and the corresponding computational formulas are given based on the new matrix expression. By utilizing the matrix STP approach, we can obtain the necessary and sufficient conditions to implement the static state output feedback stabilization for NDFA. Meanwhile, starting from the matrix STP, we designed a systematic procedure to seek the controller through an extended output feedback feasible event set. Finally, an illustrative example is provided to prove the efficacy of newly proposed method. Current results are conducive to better understand and devise the effective finite automata for discrete event systems.