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Pole Assignment in Hybrid Differential-Difference Systems

Pole Assignment in Hybrid Differential-Difference Systems We present a general approach to the pole assignment problem for linear stationary hybrid differential-difference systems as a coefficient control problem for their characteristic equations. Various scales (classes) of linear feedback controllers are considered. Special attention is paid to the solvability of the pole assignment problem for such systems in the scale of general differential-difference controllers and in a general scale that, along with differential-difference controllers, contains integral controllers whose kernels are compactly supported functions. A general scheme for constructing such controllers is proposed based on the algebraic properties of the shift operator, the Paley–Wiener theorem on compactly supported functions, and the methods of interpolation theory in the class of entire functions of exponential type. Examples and counterexamples illustrating the results are given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Pole Assignment in Hybrid Differential-Difference Systems

Marchenko, V.
Differential Equations , Volume 54 (11) – Dec 13, 2018
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References (12)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Pleiades Publishing, Inc.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266118110071
Publisher site
See Article on Publisher Site

Abstract

We present a general approach to the pole assignment problem for linear stationary hybrid differential-difference systems as a coefficient control problem for their characteristic equations. Various scales (classes) of linear feedback controllers are considered. Special attention is paid to the solvability of the pole assignment problem for such systems in the scale of general differential-difference controllers and in a general scale that, along with differential-difference controllers, contains integral controllers whose kernels are compactly supported functions. A general scheme for constructing such controllers is proposed based on the algebraic properties of the shift operator, the Paley–Wiener theorem on compactly supported functions, and the methods of interpolation theory in the class of entire functions of exponential type. Examples and counterexamples illustrating the results are given.

Journal

Differential Equations – Springer Journals

Published: Dec 13, 2018

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