Controllability issues of discrete-time linear systems with a state time-delay

This paper deals with the controllability of discrete-time linear systems with a time-invariant delay in state. As an improvement to existing definitions, a new controllability definition, which implies stabilizability and the existence of feedback controller for eigenvalue assignment, is introduced first. Then a necessary and sufficient criterion is developed to check the controllability. With this criterion the controllability and stabilizability of systems with a state delay can be properly checked.