On the static output feedback stabilization of deterministic finite automata based upon the approach of semi-tensor product of matrix

Abstract

In this paper, the static output feedback stabilization (SOFS) of deterministic finite automata (DFA) via the semi-tensor product (STP) of matrices is investigated. Firstly, the matrix expression of Moore-type automata is presented by using STP. Here the concept of the set of output feedback feasible events (OFFE) is introduced and expressed in the vector form, and the stabilization of DFA is defined in the sense of static output feedback (SOF) control. Secondly, SOFS problem of DFA is investigated within the framework of STP, including single-equilibrium-based SOFS, multi-equilibrium-based SOFS, and further limit cycle-based SOFS. Then the necessary and sufficient conditions for the existence of the three types SOFS are proposed respectively. Meanwhile the efficient and systematic procedures based on the matrix theory to seek the corresponding SOF controller are provided for the three types SOFS problem. Finally, two examples are presented to illustrate the effectiveness of the proposed approach.