TY - JOUR

T1 - Lyapunov stability tests for integral delay systems

AU - Егоров, Алексей Валерьевич

AU - Mondie, S.

AU - Ortiz, Reynaldo

PY - 2025

Y1 - 2025

N2 - An overview of stability conditions in terms of the Lyapunov matrix for linear integral delay equations is presented. Several examples in the analysis, control and modeling motivate their study. In the framework of Lyapunov–Krasovskii functionals with prescribed derivatives, we review the stability theorems for these functionals and prove a stability criterion (necessary and sufficient condition) in terms of the system delay Lyapunov matrix. The organization of the paper and the detailed developments have the purpose of serving as a tutorial. As a new result, we prove that the stability criterion can be tested in a finite number of operations. Finally, we suggest future directions of research in the field, in particular, the reduction of the bound for which sufficiency is guaranteed and the extension to more general classes of systems.

AB - An overview of stability conditions in terms of the Lyapunov matrix for linear integral delay equations is presented. Several examples in the analysis, control and modeling motivate their study. In the framework of Lyapunov–Krasovskii functionals with prescribed derivatives, we review the stability theorems for these functionals and prove a stability criterion (necessary and sufficient condition) in terms of the system delay Lyapunov matrix. The organization of the paper and the detailed developments have the purpose of serving as a tutorial. As a new result, we prove that the stability criterion can be tested in a finite number of operations. Finally, we suggest future directions of research in the field, in particular, the reduction of the bound for which sufficiency is guaranteed and the extension to more general classes of systems.

KW - integral delay system

KW - stability criterion

KW - Lyapunov matrix

KW - integral delay system

KW - stability criterion

KW - Lyapunov matrix

KW - Integral delay system

KW - Stability criterion

UR - https://www.mendeley.com/catalogue/86091f02-2863-310b-af91-507a910055f9/

U2 - 10.1016/j.arcontrol.2024.100985

DO - 10.1016/j.arcontrol.2024.100985

M3 - Article

VL - 59

JO - Annual Reviews in Control

JF - Annual Reviews in Control

SN - 1367-5788

M1 - 100985

ER -