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Finite spectrum assignment problem for systems with delays
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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“The proof hinges on a fixed-point argument detailed in our prior conference paper [38], where an identical target system was analyzed.”
From Multi-layer predictor feedback design for nonlinear integro-differential equations with state-dependent input delays (2026) · cites this paper as [38]
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Metadata
- Authors
- Manitius, A., & Olbrot, A.
- Affiliations
- Centre de recherches mathématiques (CA)
- Warsaw University of Technology (PL)
- Venue
- IEEE Transactions on Automatic Control
- Published
- 1979-08
- Volume
- 24
- Issue
- 4
- Pages
- 541-552
- ISSN
- 0018-9286 (ISSN-L)
- 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
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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