Cited by 1,140Stability and Control of Uncertain SystemsAdvanced Control Systems DesignStability and Controllability of Differential Equations

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Finite spectrum assignment problem for systems with delays

Manitius, A., Olbrot, A.·1979·IEEE Transactions on Automatic Control

DOI 10.1109/tac.1979.1102124

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Abstract

In this paper linear systems with delays in state and/or control variables are considered. The objective is to design a feedback law which yields a finite spectrum of the closed-loop system, located at an arbitrarily preassigned set ofnpoints in the complex plane. It is shown that in case of systems with delays in control only the problem is solvable if and only if some function space controllability criterion is met. The solution is then easily obtainable by standard spectrum assignment methods, while the resulting feedback law involves integrals over the past control. In case of delays in state variables it is shown that a technique based on the finite Laplace transform, related to a recent work on function space controllability, leads to a constructive design procedure. The resulting feedback consists of proportional and (finite interval) integral terms over present and past values of state variables. Some indications on how to combine these results in case of systems including both state and control delays are given. Sensitivity of the design to parameter variations is briefly analyzed.

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Authors: Manitius, A., & Olbrot, A.
Affiliations: Centre de recherches mathématiques (CA)
Warsaw University of Technology (PL)
Venue: IEEE Transactions on Automatic Control
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Published: 1979-08
Volume: 24
Issue: 4
Pages: 541-552
ISSN: 0018-9286 (ISSN-L)
DOI: 10.1109/tac.1979.1102124
OpenAlex: W2070065489
Cited by: 1,140
References: 11
Citations by year: 2026: 17 · 2025: 40 · 2024: 33 · 2023: 29 · 2022: 52 · 2021: 49 · 2020: 51 · 2019: 58 · 2018: 49 · 2017: 49 · 2016: 57 · 2015: 57 · 2014: 75 · 2013: 39 · 2012: 42
FWCI: 21.50
Type: journal article
Language: en
Open access: closed
Licence: ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html (vor)
Locations: IEEE Transactions on Automatic Control (publishedVersion)
Topics: Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Design
Physical Sciences › Engineering › Control and Systems Engineering › Stability and Controllability of Differential Equations
Keywords: finite spectrum assignment, time-delay systems, state delay, control delay, feedback control design, integral feedback, closed-loop eigenvalues

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Finite spectrum assignment problem for systems with delays

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