Predictor-feedback prescribed-time stabilization of LTI systems with input delay
Open accessAbstract
This article first deals with the problem of prescribed-time stability of linear systems without delay. The analysis and design involve theBell polynomials,the generalized Laguerre polynomials,the Lah numbers, and a suitablepolynomial-based Vandermonde matrix. The results can be used to design a new controller—with time-varying gains—ensuring prescribed-time stabilization of controllable linear time-invariant (LTI) systems. The approach leads to similar results compared to Hollowayet al.2019, but offers an alternative and compact control design (especially for the choice of the time-varying gains). Based on the preliminary results for the delay-free case, we then study controllable LTI systems with single input and subject to a constant input delay. We design a predictor feedback with time-varying gains. To achieve this, we model the input delay as a transport partial differential equation (PDE) and build on the cascade PDE–ordinary differential equation setting (inspired by Krstic 2009) so as the design of the prescribed-time predictor feedback is carried out based on the backstepping approach, which makes use oftime-varying kernels. We guarantee the bounded invertibility of the backstepping transformation, and we prove that the closed-loop solution converges to the equilibrium in a prescribed time. A simulation example illustrates the results.
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For any setpoint Q* in [0, min{Qmax, μ}] and any chosen setpoint slope S(Q*) ≥ Smin(Q*), taking the control gains (Λl, Λr) as solutions of the fixed-point equations makes the closed-loop system consisting of (84) with initial condition Q0 in [0, min{Qmax, μ}] and control law (85) asymptotically stable.
“the closed-loop system consisting of (84) with an initial condition Q 0 ∈ [ 0 , min { Q max , µ } ] and control law (85) is asymptotically stable.”
From Multi-layer predictor feedback design for nonlinear integro-differential equations with state-dependent input delays (2026) · cites this paper as [18]
Unlike prior work [18] and [14] that establishes globally stabilizing safe softened bang-bang control under predictor feedback, the present setting admits only local guarantees due to the presence of source terms.
“In contrast to [18] and [14], which establish globally stabilizing, safe softened bang-bang control under a predictor feedback design, the present setting admits only local guarantees due to the presence of source terms.”
From Multi-layer predictor feedback design for nonlinear integro-differential equations with state-dependent input delays (2026) · cites this paper as [18]
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- Authors
- Espitia, N., & Perruquetti, W.
- Affiliations
- Centre de Recherche en Informatique, Signal et Automatique de Lille, CNRS, Centrale Lille, Université de Lille, Lille, France
- Centre National de la Recherche Scientifique (FR)
- Venue
- IEEE Transactions on Automatic Control
- Published
- 2022-06
- Volume
- 67
- Issue
- 6
- Pages
- 2784-2799
- ISSN
- 0018-9286 (ISSN-L)
- 1558-2523
- 2334-3303
- OpenAlex
- W3176155799
- Cited by
- 63
- References
- 43
- Citations by year
- 2026: 10 · 2025: 12 · 2024: 17 · 2023: 9 · 2022: 9 · 2021: 5 · 2020: 1
- FWCI
- 4.45
- Type
- journal article
- Language
- en
- Open access
- green
- hal.science
- Licence
- Locations
- IEEE Transactions on Automatic Control (publishedVersion)
- HAL (submittedVersion, other-oa)
- LillOA (Université de Lille (University Of Lille)) (submittedVersion, other-oa)
- Funders
- Agence Nationale de la Recherche (ANR 15-CE23-0007)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Controllability of Differential Equations
- Physical Sciences › Engineering › Control and Systems Engineering › Adaptive Control of Nonlinear Systems
- Keywords
- prescribed-time stabilization, predictor feedback, input delay, linear time-invariant systems, Bell polynomials, generalized Laguerre polynomials, Lah numbers, Vandermonde matrix, time-varying gain, backstepping control, single-input systems
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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