TY - JOUR

T1 - A new stability criterion and its application to robust stability analysis for linear systems with distributed delays

AU - Кудряков, Дмитрий Александрович

AU - Александрова, Ирина Васильевна

PY - 2023/6/1

Y1 - 2023/6/1

N2 - 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.

AB - 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.

KW - Linear systems

KW - Lyapunov matrices

KW - Lyapunov–Krasovskii functionals

KW - Razumikhin condition

KW - Robust stability

KW - Stability

KW - Time delay

UR - https://www.mendeley.com/catalogue/f9c5fce3-d62c-32fe-9f79-d51dd1174de5/

U2 - 10.1016/j.automatica.2023.110973

DO - 10.1016/j.automatica.2023.110973

M3 - Article

VL - 152

JO - Automatica

JF - Automatica

SN - 0005-1098

M1 - 110973

ER -