Controllability, reachability, stabilizability and state reduction in automata

The authors present a state-equation-like approach to automata, which is used to model discrete event systems (DES). They define controllability, reachability and stabilizability in the usual manner and provide theorems to test these properties. Divisibility for matrices in Boolean algebra is defined. A theorem which determines if a given transformation to a reduce automaton is valid or not is proposed. It is claimed that the analogies in the concepts and setting help in the transfer of approaches in control theory to the area of DES control and also aid in hybrid system formulations.