A Note on Relative Controllability of Higher Order Linear Delayed Discrete Systems

This article is concerned with relative controllability of higher order linear discrete delayed systems with a single delay. By a formula that uses special matrix functions (discrete delayed matrix sine and cosine) to compute the solution of the initial problem, a criterion is found for relative controllability. In terms of special matrix functions, a control function is constructed to solve the problem of relative controllability. It is shown that the transformation of a given system into a higher dimensional system without delays leads to a nonequivalent problem of relative controllability. The results are illustrated by an example.