TY - JOUR

T1 - Necessary and sufficient stability conditions for integral delay systems

AU - Ortiz, Reynaldo

AU - Egorov, Alexey

AU - Mondié, Sabine

N1 - Publisher Copyright: © 2021 John Wiley & Sons Ltd.

PY - 2022/4

Y1 - 2022/4

N2 - A Lyapunov–Krasovskii functional with prescribed derivative whose construction does not require the stability of the system is introduced. It leads to the presentation of stability/instability theorems. By evaluating the functional at initial conditions depending on the fundamental matrix we are able to present necessary and sufficient stability conditions expressed exclusively in terms of the delay Lyapunov matrix for integral delay systems. Some examples illustrate and validate the stability conditions.

AB - A Lyapunov–Krasovskii functional with prescribed derivative whose construction does not require the stability of the system is introduced. It leads to the presentation of stability/instability theorems. By evaluating the functional at initial conditions depending on the fundamental matrix we are able to present necessary and sufficient stability conditions expressed exclusively in terms of the delay Lyapunov matrix for integral delay systems. Some examples illustrate and validate the stability conditions.

KW - functionals

KW - integral delay systems

KW - Lyapunov matrix

KW - renewal equation

KW - stability

KW - LINEAR-SYSTEMS

KW - EPIDEMIC MODELS

KW - DIFFERENCE-EQUATIONS

KW - NEUTRAL-TYPE SYSTEMS

UR - http://www.scopus.com/inward/record.url?scp=85119668256&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/e4604635-ae81-3509-8d50-c1207aaad4f6/

U2 - 10.1002/rnc.5907

DO - 10.1002/rnc.5907

M3 - Article

AN - SCOPUS:85119668256

VL - 32

SP - 3152

EP - 3174

JO - International Journal of Robust and Nonlinear Control

JF - International Journal of Robust and Nonlinear Control

SN - 1049-8923

IS - 6

ER -