Computation of the Lyapunov matrix for periodic time-delay systems and its application to robust stability analysis

Marco A. Gomez, Alexey V. Egorov, Sabine Mondié, Alexey P. Zhabko

Research output

Abstract

A new procedure for computing the delay Lyapunov matrix for periodic time-delay systems that is based on the numerical solution of a partial differential equations (PDE) system is presented. The introduction of a new set of boundary conditions that are satisfied by the PDE system allows us to propose a new methodology for computing the initial conditions required by the implemented numerical scheme. The potential of the presented results is demonstrated by obtaining robust stability conditions depending on the delay Lyapunov matrix with respect to the system parameters, the delay and the frequency. The theoretical results are applied to the widely known delayed Mathieu equation.

Original languageEnglish
Article number104501
JournalSystems and Control Letters
Volume132
DOIs
Publication statusPublished - 1 Oct 2019

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Partial differential equations
Time delay
Boundary conditions
Robust stability

Scopus subject areas

  • Control and Systems Engineering
  • Computer Science(all)
  • Mechanical Engineering
  • Electrical and Electronic Engineering

Cite this

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title = "Computation of the Lyapunov matrix for periodic time-delay systems and its application to robust stability analysis",
abstract = "A new procedure for computing the delay Lyapunov matrix for periodic time-delay systems that is based on the numerical solution of a partial differential equations (PDE) system is presented. The introduction of a new set of boundary conditions that are satisfied by the PDE system allows us to propose a new methodology for computing the initial conditions required by the implemented numerical scheme. The potential of the presented results is demonstrated by obtaining robust stability conditions depending on the delay Lyapunov matrix with respect to the system parameters, the delay and the frequency. The theoretical results are applied to the widely known delayed Mathieu equation.",
keywords = "Delayed Mathieu equation, Lyapunov matrix, Lyapunov–Krasovskii functionals, Periodic delay systems, Robust stability analysis",
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T1 - Computation of the Lyapunov matrix for periodic time-delay systems and its application to robust stability analysis

AU - Gomez, Marco A.

AU - Egorov, Alexey V.

AU - Mondié, Sabine

AU - Zhabko, Alexey P.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - A new procedure for computing the delay Lyapunov matrix for periodic time-delay systems that is based on the numerical solution of a partial differential equations (PDE) system is presented. The introduction of a new set of boundary conditions that are satisfied by the PDE system allows us to propose a new methodology for computing the initial conditions required by the implemented numerical scheme. The potential of the presented results is demonstrated by obtaining robust stability conditions depending on the delay Lyapunov matrix with respect to the system parameters, the delay and the frequency. The theoretical results are applied to the widely known delayed Mathieu equation.

AB - A new procedure for computing the delay Lyapunov matrix for periodic time-delay systems that is based on the numerical solution of a partial differential equations (PDE) system is presented. The introduction of a new set of boundary conditions that are satisfied by the PDE system allows us to propose a new methodology for computing the initial conditions required by the implemented numerical scheme. The potential of the presented results is demonstrated by obtaining robust stability conditions depending on the delay Lyapunov matrix with respect to the system parameters, the delay and the frequency. The theoretical results are applied to the widely known delayed Mathieu equation.

KW - Delayed Mathieu equation

KW - Lyapunov matrix

KW - Lyapunov–Krasovskii functionals

KW - Periodic delay systems

KW - Robust stability analysis

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DO - 10.1016/j.sysconle.2019.104501

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VL - 132

JO - Systems and Control Letters

JF - Systems and Control Letters

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