Controllability Analysis of Linear Discrete Time Systems with Time Delay in State

Abstract

The controllability issues for linear discrete-time systems with delay in state are addressed. By introducing a new concept, the minimum controllability realization index (MinCRI), the characteristic of controllability is revealed. It is proved that the MinCRI of a system with state delay exists and is finite. Based on this result, a necessary and sufficient condition for the controllability of discrete-time linear systems with state delay is established.