Stability Analysis of Some Types of Singularly Perturbed Time-Delay Differential Systems: Symmetric Matrix Riccati Equation Approach

被引：1

作者：

Glizer, Valery Y. ^{[1
]}

机构：

[1] Braude Coll Engn, Galilee Res Ctr Appl Math, IL-2161002 Karmiel, Israel

来源：

SYMMETRY-BASEL | 2024年 / 16卷 / 07期

关键词：

time-delay differential system; singularly perturbed system; asymptotic stability; symmetric matrix Riccati equation method; partial slow-fast decomposition; parameter-free stability conditions; SLOW-FAST DECOMPOSITION; EXPONENTIAL STABILITY; STABILIZATION;

D O I：

10.3390/sym16070838

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Several types of linear and nonlinear singularly perturbed time-delay differential systems are considered. Asymptotic stability of the linear systems and asymptotic stability of the trivial solution of the nonlinear systems, valid for any sufficiently small value of the parameter of singular perturbation, are analyzed. For the stability analysis in the linear case, a partial exact slow-fast decomposition of the original system and an application of the Symmetric Matrix Riccati Equation method are proposed. Such an analysis yields parameter-free conditions, providing the asymptotic stability of the considered linear singularly perturbed time-delay differential systems for any sufficiently small value of the parameter of singular perturbation. Using the asymptotic stability results for the considered linear systems and the method of asymptotic stability in the first approximation, parameter-free conditions, guaranteeing the asymptotic stability of the trivial solution to the considered nonlinear systems for any sufficiently small value of the parameter of singular perturbation, are derived. Illustrative examples are presented.

引用

页数：35

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