Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2018, Article ID 6719319, 6 pages
https://doi.org/10.1155/2018/6719319
Research Article

Controllability, Reachability, and Stabilizability of Finite Automata: A Controllability Matrix Method

1School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
2Institute of Data Science and Technology, Shandong Normal University, Jinan 250014, China

Correspondence should be addressed to Haitao Li; moc.liamg@90iloatiah

Received 15 November 2017; Revised 6 January 2018; Accepted 18 January 2018; Published 28 February 2018

Academic Editor: Alessandro Lo Schiavo

Copyright © 2018 Yalu Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper investigates the controllability, reachability, and stabilizability of finite automata by using the semitensor product of matrices. Firstly, by expressing the states, inputs, and outputs as vector forms, an algebraic form is obtained for finite automata. Secondly, based on the algebraic form, a controllability matrix is constructed for finite automata. Thirdly, some necessary and sufficient conditions are presented for the controllability, reachability, and stabilizability of finite automata by using the controllability matrix. Finally, an illustrative example is given to support the obtained new results.