Advances in Study of Time-Delay Systems and Their Applications, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 3966

Special Issue Editor


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Guest Editor
1. Department of Automation and Control Engineering, Faculty of Applied Informatics, Tomas Bata University in Zlín, 760 01 Zlín, Czech Republic
2. Department of Technical Studies, College of Polytechnics Jihlava, Tolstého 1556, 586 01 Jihlava, Czech Republic
Interests: control system synthesis; PI control; closed loop systems; delays; frequency-domain analysis; linear systems; polynomials; robust control; stability; MIMO systems; active disturbance rejection control; aerospace components; aircraft control; approximation theory; asymptotic stability; chemical reactors; decentralised control; delay systems; discrete time systems; feedback; invariance; multivariable control systems; optimal control; polynomial approximation; three-term control
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Special Issue Information

Dear Colleagues,

In dynamical systems, the delay phenomenon is a generic part of industrial, communication, economical, biological, and similar processes that considerably affects their stability and dynamics. Moreover, it unambiguously deteriorates the quality of control performance in feedback loops. The study of the influence of delays on system stability, dynamics, and control performance poses a challenging mathematic exercise. System and control theories have worked to tackle this issue for almost a century, since the publication of the famous work by Volterra (1928). Modern theory is confronted with increasing requirements for the quality and performance of control systems in the industry, as well as in everyday reality, which can hardly be achieved using conventional methods. In order to meet these goals, more in-depth knowledge of the controlled delayed systems is a prerequisite.

This Special Issue of Mathematics is focused on recent developments in approaches to time-delay systems analysis and control design. We seek papers on system stability and dynamics analysis, including exponential, asymptotic, strong, delay-dependent, delay-independent, BIBO, H2, H∞, and other types of system stability. Hopf, fold, and pitchfork bifurcation; stability switching; and eigenvalue analyses are also welcome. Special consideration will be given to delays of neutral types and systems given by algebraic-differential equations; however, systems with retarded delays are also acceptable. In addition, the scope of this Special Issue includes modern control methods and their applications, such as switched systems, event-triggered control, Lyapunov–Razumikhin- and Krasovskii-type approaches, etc.

All submitted papers will be peer reviewed and selected on the basis of their quality and relevance to this Special Issue.

Dr. Libor Pekař
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • time-invariant and time-variant delayed systems
  • delay-varying models and their stability
  • linear and nonlinear delayed systems
  • dynamics and stability of systems with retarded and neutral delays
  • delayed systems described by algebraic-differential equations
  • exponential, asymptotic, strong, BIBO, H2, H∞ stability of time-delay systems
  • Hopf, fold, and pitchfork bifurcation, stability switching, and eigenvalue analysis
  • delay-dependent and delay-independent stability
  • finite dimension approximations
  • filtering and estimation of time-delay systems
  • switched systems with time delay and event-triggered control
  • Krasovskii-type and Lyapunov–Razumikhin-type stability and control approaches
  • new results in controllability and observability of time-delay systems
  • robust, algebraic, and adaptive control methods and their applications

Published Papers (4 papers)

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Research

18 pages, 1022 KiB  
Article
Delay-Embedding Spatio-Temporal Dynamic Mode Decomposition
by Gyurhan Nedzhibov
Mathematics 2024, 12(5), 762; https://doi.org/10.3390/math12050762 - 04 Mar 2024
Viewed by 648
Abstract
Spatio-temporal dynamic mode decomposition (STDMD) is an extension of dynamic mode decomposition (DMD) designed to handle spatio-temporal datasets. It extends the framework so that it can analyze data that have both spatial and temporal variations. This facilitates the extraction of spatial structures along [...] Read more.
Spatio-temporal dynamic mode decomposition (STDMD) is an extension of dynamic mode decomposition (DMD) designed to handle spatio-temporal datasets. It extends the framework so that it can analyze data that have both spatial and temporal variations. This facilitates the extraction of spatial structures along with their temporal evolution. The STDMD method extracts temporal and spatial development information simultaneously, including wavenumber, frequencies, and growth rates, which are essential in complex dynamic systems. We provide a comprehensive mathematical framework for sequential and parallel STDMD approaches. To increase the range of applications of the presented techniques, we also introduce a generalization of delay coordinates. The extension, labeled delay-embedding STDMD allows the use of delayed data, which can be both time-delayed and space-delayed. An explicit expression of the presented algorithms in matrix form is also provided, making theoretical analysis easier and providing a solid foundation for further research and development. The novel approach is demonstrated using some illustrative model dynamics. Full article
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9 pages, 262 KiB  
Article
Asymptotic Behavior of Solutions in Nonlinear Neutral System with Two Volterra Terms
by Mouataz Billah Mesmouli, Abdelouaheb Ardjouni and Hicham Saber
Mathematics 2023, 11(12), 2676; https://doi.org/10.3390/math11122676 - 13 Jun 2023
Viewed by 729
Abstract
In this manuscript, we generalise previous results in the literature by providing sufficient conditions for the matrix measure to guarantee the stability, asymptotic stability and exponential stability of a neutral system of differential equations. This is achieved by constructing a suitable operator from [...] Read more.
In this manuscript, we generalise previous results in the literature by providing sufficient conditions for the matrix measure to guarantee the stability, asymptotic stability and exponential stability of a neutral system of differential equations. This is achieved by constructing a suitable operator from our system and applying the Banach fixed point theorem. Full article
26 pages, 1361 KiB  
Article
Criteria on Exponential Incremental Stability of Dynamical Systems with Time Delay
by Yingying Lang and Wenlian Lu
Mathematics 2023, 11(10), 2242; https://doi.org/10.3390/math11102242 - 10 May 2023
Viewed by 697
Abstract
Incremental stability analysis for time-delay systems has attracted more and more attention for its contemporary applications in transportation processes, population dynamics, economics, satellite positions, etc. This paper researches the criteria for exponential incremental stability for time-delay systems with continuous or discontinuous right-hand sides. [...] Read more.
Incremental stability analysis for time-delay systems has attracted more and more attention for its contemporary applications in transportation processes, population dynamics, economics, satellite positions, etc. This paper researches the criteria for exponential incremental stability for time-delay systems with continuous or discontinuous right-hand sides. Firstly, the sufficient conditions for exponential incremental stability for time-delay systems with continuous right-hand sides are studied, and several corollaries for specific cases are provided. As for time-delay systems with discontinuous right-hand sides, after expounding the relevant conditions for the existence and uniqueness of the Filippov solution, by using approximation methods, sufficient conditions for exponential incremental stability are obtained. The conclusions are applied to linear switched time-delay systems and Hopfield neural network systems with composite right-hand sides. Full article
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15 pages, 404 KiB  
Article
Exponential Stability of Nonlinear Time-Varying Delay Differential Equations via Lyapunov–Razumikhin Technique
by Natalya O. Sedova and Olga V. Druzhinina
Mathematics 2023, 11(4), 896; https://doi.org/10.3390/math11040896 - 10 Feb 2023
Cited by 1 | Viewed by 1266
Abstract
In this article, some new sufficient conditions for the exponential stability of nonlinear time-varying delay differential equations are given. An extension of the classical asymptotical stability theorem in terms of a Lyapunov–Razumikhin function is obtained. The condition of non-positivity of the time derivative [...] Read more.
In this article, some new sufficient conditions for the exponential stability of nonlinear time-varying delay differential equations are given. An extension of the classical asymptotical stability theorem in terms of a Lyapunov–Razumikhin function is obtained. The condition of non-positivity of the time derivative of a Razumikhin function is weakened. Additionally, the resulting sufficient asymptotic stability conditions allow us to guarantee uniform exponential stability and evaluate the exponential convergence rate of the system solutions. The effectiveness of the results is demonstrated by some examples. Full article
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