Generalized Halanay inequality and its application to delay differential inclusions

被引：1

作者：

Zhang, Zhenxing ^{[1
]}

Chen, Huabin ^{[1
]}

Zhu, Honglin ^{[1
]}

机构：

[1] Nanchang Univ, Dept Math, Nanchang 330031, Jiangxi, Peoples R China

来源：

AUTOMATICA | 2024年 / 166卷

基金：

中国国家自然科学基金;

关键词：

Generalized Halanay inequality; Differential inclusions; Time -varying delay; Uniformly ultimate boundedness; Stability analysis; STABILITY ANALYSIS; ASYMPTOTIC STABILITY; DYNAMICAL-SYSTEMS; TIME;

D O I：

10.1016/j.automatica.2024.111704

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this work, by using a generalized Halanay inequality, a regular Lyapunov function and the theory of nonsmooth analysis, we investigate the uniformly ultimate boundedness of the zero solution for nonautonomous delay differential inclusions. The sufficient condition is presented in integral form, which is different from the ones given in some related literature. We also provide different characterizations of the sufficient conditions on the stability, the asymptotic stability, and the exponential stability of the zero solution for nonautonomous delay differential inclusions. Finally, one example is given to illustrate the effectiveness of the theoretical results obtained. (c) 2024 Elsevier Ltd. All rights reserved.

引用

页数：6

共 28 条

[1]

[Anonymous], 2002, Amer. Math. Soc.

[2]

Aubin J.-P., 1984, Fundamental Principles of Mathematical Sciences, V264

[3]

Bacciotti A., 1999, ESAIM. Control, Optimisation and Calculus of Variations, V4, P361, DOI 10.1051/cocv:1999113

[4] Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability [J].

Brogliato, Bernard ;

Tanwani, Aneel .

SIAM REVIEW, 2020, 62 (01) :3-129

[5] Finite-/Fixed-Time Stability of Nonautonomous Functional Differential Inclusion: Lyapunov Approach Involving Indefinite Derivative [J].

Cai, Zuowei ;

Huang, Lihong ;

Wang, Zengyun .

IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2022, 33 (11) :6763-6774

[6] Novel Fixed-Time Stability Criteria for Discontinuous Nonautonomous Systems: Lyapunov Method With Indefinite Derivative [J].

Cai, Zuowei ;

Huang, Lihong ;

Wang, Zengyun .

IEEE TRANSACTIONS ON CYBERNETICS, 2022, 52 (06) :4286-4299

[7] Generalized Lyapunov approach for functional differential inclusions [J].

Cai, Zuowei ;

Huang, Lihong .

AUTOMATICA, 2020, 113

[8] GENERALIZED LYAPUNOV-RAZUMIKHIN METHOD FOR RETARDED DIFFERENTIAL INCLUSIONS: APPLICATIONS TO DISCONTINUOUS NEURAL NETWORKS [J].

Cai, Zuowei ;

Huang, Jianhua ;

Huang, Lihong .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2017, 22 (09) :3591-3614

[9]

Ceregioli F. M., 1999, Ph.D. thesis

[10]

Clarke F.H., 1998, Nonsmooth Analysis and Control Theory

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