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Hyperexponential and Fixed-Time Stability of Time-Delay Systems: Lyapunov–Razumikhin Method

Authors :
Artem N. Nekhoroshikh
Denis Efimov
Andrey Polyakov
Wilfrid Perruquetti
Igor B. Furtat
National Research University of Information Technologies, Mechanics and Optics [St. Petersburg] (ITMO)
Finite-time control and estimation for distributed systems (VALSE)
Inria Lille - Nord Europe
Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL)
Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL)
Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)
Institute of Mechanical Engineering Problems [St. Petersburg] (IPME)
Russian Academy of Sciences [Moscow] (RAS)
The results of Section IV are supported by the Russian Science Foundation under grant no. 18-79-10104 (https://rscf.ru/en/project/18-79-10104/) at IPME RAS. The results of Section V are supported by the Russian Science Foundation under grant no. 21-71-10032 at ITMO University.
Source :
IEEE Transactions on Automatic Control, IEEE Transactions on Automatic Control, In press, ⟨10.1109/tac.2022.3168487⟩
Publication Year :
2023
Publisher :
Institute of Electrical and Electronics Engineers (IEEE), 2023.

Abstract

International audience; Razumikhin-like theorems on hyperexponential and fixed-time stability of time-delay systems are proposed for both explicitly and implicitly defined Lyapunov functions. While the former method is useful for stability analysis, the latter approach is more suitable for control synthesis. Examples of systems that can be stabilized hyperexponentially and in fixed time are given. The control parameters tuning algorithm is presented in the form of linear matrix inequalities. The numerical simulations illustrate the theoretical results.

Subjects

Subjects :
implicit theorem
Lyapunov-Razumikhin theorem
Control and Systems Engineering
Fixed-time and hyperexponential stability
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
Electrical and Electronic Engineering
linear matrix inequalities
time-delay systems
[SPI.AUTO]Engineering Sciences [physics]/Automatic
Computer Science Applications

Details

ISSN :
23343303 and 00189286
Volume :
68
Database :
OpenAIRE
Journal :
IEEE Transactions on Automatic Control
Accession number :
edsair.doi.dedup.....89bd41220c9895ec40cf677146d24724

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