TY - JOUR

T1 - Lyapunov Direct Method for Homogeneous Time Delay Systems

AU - Жабко, Алексей Петрович

AU - Alexandrova, Irina V.

PY - 2019

Y1 - 2019

N2 - In this note, nonlinear time delay systems with homogeneous right-hand sides of degree greater than one and a constant delay are studied. Under an assumption that the corresponding delay free system is asymptotically stable, two criteria for asymptotic stability of the trivial solution based on the Lyapunov-Krasovskii functionals are presented. The first of them is a converse of the well-known Krasovskii theorem under the mentioned assumption whereas in the second one the functional is required to admit a positive definite lower bound on the set of functions satisfying a special condition of Razumikhin type only. The Lyapunov-Krasovskii functionals, which satisfy the conditions of these criteria and are universal within the class of systems under consideration, are constructed. These functionals are based on the Lyapunov functions suitable for analysis of the corresponding delay free systems. They are applied to estimation of the attraction region of solutions of homogeneous systems. Copyright (C) 2019. The Authors. Published by Elsevier Ltd. All rights reserved.

AB - In this note, nonlinear time delay systems with homogeneous right-hand sides of degree greater than one and a constant delay are studied. Under an assumption that the corresponding delay free system is asymptotically stable, two criteria for asymptotic stability of the trivial solution based on the Lyapunov-Krasovskii functionals are presented. The first of them is a converse of the well-known Krasovskii theorem under the mentioned assumption whereas in the second one the functional is required to admit a positive definite lower bound on the set of functions satisfying a special condition of Razumikhin type only. The Lyapunov-Krasovskii functionals, which satisfy the conditions of these criteria and are universal within the class of systems under consideration, are constructed. These functionals are based on the Lyapunov functions suitable for analysis of the corresponding delay free systems. They are applied to estimation of the attraction region of solutions of homogeneous systems. Copyright (C) 2019. The Authors. Published by Elsevier Ltd. All rights reserved.

KW - Time delay systems

KW - asymptotic stability

KW - Lyapunov-Krasovskii functionals homogeneous systems

KW - attraction region

KW - ROBUST STABILITY ANALYSIS

KW - INDEPENDENT STABILITY

KW - KRASOVSKII

KW - RAZUMIKHIN

U2 - 10.1016/j.ifacol.2019.12.210

DO - 10.1016/j.ifacol.2019.12.210

M3 - статья

VL - 52

SP - 79

EP - 84

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8971

IS - 18

Y2 - 9 September 2019 through 11 September 2019

ER -