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

• Published in: IEEE transactions on automatic control Vol. 65; no. 12; pp. 5472 - 5479
• Main Authors: Diblik, Josef, Mencakova, Kristyna
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-12-2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Control function; Controllability; Delays; discrete delayed cosine; discrete delayed sine; discrete system; Discrete systems; Discrete-time systems; Mathematical model; relative controllability; Stability; Trigonometric functions
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2020.2976298

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.