Lyapunov matrices for a class of time-delay systems with piecewise-constant kernel

    Research output

    3 Citations (Scopus)

    Abstract

    In this contribution, we study time-delay systems with distributed delay whose kernel is piecewise constant. It is shown that the problem of finding a Lyapunov matrix for this class of time-delay systems can be reduced to the computation of solutions to an auxiliary system of linear differential equations with boundary conditions. The problem of solving the auxiliary system is then reduced to the solution of a system of linear algebraic equations. It is established that the auxiliary system with boundary conditions admits a unique solution if and only if there exists a unique Lyapunov matrix.

    Original languageEnglish
    Pages (from-to)1298-1305
    Number of pages8
    JournalInternational Journal of Control
    Volume92
    Issue number6
    DOIs
    Publication statusPublished - 3 Jun 2019

    Fingerprint

    Time-delay Systems
    Lyapunov
    Time delay
    Boundary conditions
    kernel
    Linear equations
    Differential equations
    Distributed Delay
    Linear differential equation
    Algebraic Equation
    Unique Solution
    Linear equation
    If and only if
    Class

    Scopus subject areas

    • Applied Mathematics
    • Computer Science Applications

    Cite this

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    title = "Lyapunov matrices for a class of time-delay systems with piecewise-constant kernel",
    abstract = "In this contribution, we study time-delay systems with distributed delay whose kernel is piecewise constant. It is shown that the problem of finding a Lyapunov matrix for this class of time-delay systems can be reduced to the computation of solutions to an auxiliary system of linear differential equations with boundary conditions. The problem of solving the auxiliary system is then reduced to the solution of a system of linear algebraic equations. It is established that the auxiliary system with boundary conditions admits a unique solution if and only if there exists a unique Lyapunov matrix.",
    keywords = "Lyapunov matrix, Lyapunov–Krasovskii functional, time-delay system, Lyapunov-Krasovskii functional",
    author = "Aliseyko, {A. N.}",
    year = "2019",
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    doi = "10.1080/00207179.2017.1390261",
    language = "English",
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    TY - JOUR

    T1 - Lyapunov matrices for a class of time-delay systems with piecewise-constant kernel

    AU - Aliseyko, A. N.

    PY - 2019/6/3

    Y1 - 2019/6/3

    N2 - In this contribution, we study time-delay systems with distributed delay whose kernel is piecewise constant. It is shown that the problem of finding a Lyapunov matrix for this class of time-delay systems can be reduced to the computation of solutions to an auxiliary system of linear differential equations with boundary conditions. The problem of solving the auxiliary system is then reduced to the solution of a system of linear algebraic equations. It is established that the auxiliary system with boundary conditions admits a unique solution if and only if there exists a unique Lyapunov matrix.

    AB - In this contribution, we study time-delay systems with distributed delay whose kernel is piecewise constant. It is shown that the problem of finding a Lyapunov matrix for this class of time-delay systems can be reduced to the computation of solutions to an auxiliary system of linear differential equations with boundary conditions. The problem of solving the auxiliary system is then reduced to the solution of a system of linear algebraic equations. It is established that the auxiliary system with boundary conditions admits a unique solution if and only if there exists a unique Lyapunov matrix.

    KW - Lyapunov matrix

    KW - Lyapunov–Krasovskii functional

    KW - time-delay system

    KW - Lyapunov-Krasovskii functional

    UR - http://www.scopus.com/inward/record.url?scp=85034214924&partnerID=8YFLogxK

    UR - http://www.mendeley.com/research/lyapunov-matrices-class-timedelay-systems-piecewiseconstant-kernel

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