A new stability criterion and its application to robust stability analysis for linear systems with distributed delays

Recently, the possibility to verify positive definiteness of Lyapunov–Krasovskii functionals only on a specific Razumikhin-type set of functions to conclude on the stability of linear time delay systems was shown. In this paper, for a class of systems with multiple concentrated and distributed delay...

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Bibliographic Details
Published inAutomatica (Oxford) Vol. 152; p. 110973
Main Authors Kudryakov, Dmitry A., Alexandrova, Irina V.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.06.2023
Subjects
Linear systems
Lyapunov matrices
Lyapunov–Krasovskii functionals
Razumikhin condition
Robust stability
Stability
Time delay
Linear systems
Stability
Robust stability
Lyapunov matrices
Lyapunov–Krasovskii functionals
Time delay
Razumikhin condition
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Summary:Recently, the possibility to verify positive definiteness of Lyapunov–Krasovskii functionals only on a specific Razumikhin-type set of functions to conclude on the stability of linear time delay systems was shown. In this paper, for a class of systems with multiple concentrated and distributed delays, we extend the result and prove that this specific set may be applied while verifying the negative definiteness of the functionals derivatives along the solutions as well. The result is applied in the robustness analysis with respect to uncertainties both in the system matrices and in the delays. It provides a simple way to prove the robust stability conditions due to obviating the need to work with indefinite derivatives of functionals along the solutions of a perturbed system. As a by-product, the estimates for an unstable eigenvalue of the system are derived, and the functionals defined on complex-valued initial functions are presented.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2023.110973