A nonlinear version of Halanay's inequality for the uniform convergence to the origin

IF 1 4区数学 Q1 MATHEMATICS

Mathematical Control and Related Fields Pub Date : 2021-01-01 DOI:10.3934/mcrf.2021045

P. Pepe

引用次数: 11

Abstract

A nonlinear version of Halanay's inequality is studied in this paper as a sufficient condition for the convergence of functions to the origin, uniformly with respect to bounded sets of initial values. The same result is provided in the case of forcing terms, for the uniform convergence to suitable neighborhoods of the origin. Related Lyapunov methods for the global uniform asymptotic stability and the input-to-state stability of systems described by retarded functional differential equations, with possibly nonconstant time delays, are provided. The relationship with the Razumikhin methodology is shown.

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一致收敛到原点的哈拉奈不等式的一个非线性版本

本文研究了Halanay不等式的一个非线性形式，作为函数关于有界初值集一致收敛于原点的充分条件。对于强迫项，对于原点的合适邻域的一致收敛，给出了相同的结果。给出了用时滞泛函微分方程描述的可能具有非常时滞的系统的全局一致渐近稳定性和输入状态稳定性的相关Lyapunov方法。图中显示了与Razumikhin方法的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Control and Related Fields MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

8.30%

发文量

期刊介绍： MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.