Quantitative bounds for general Razumikhin-type functional differential inequalities with applications

被引：2

作者：

Zhao, Xueyan ^{[1
]}

Fu, Minyue ^{[2
,3
]}

Deng, Feiqi ^{[1
]}

Yang, Qigui ^{[4
]}

机构：

[1] South China Univ Technol, Sch Automat Sci & Engn, Guangzhou 510641, Peoples R China

[2] Univ Newcastle, Sch Elect Engn & Comp Sci, Callaghan, NSW 2308, Australia

[3] Guangdong Univ Technol, Sch Automat, Guangzhou 510006, Peoples R China

[4] South China Univ Technol, Sch Math, Guangzhou 510641, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2020年 / 86卷

基金：

中国国家自然科学基金;

关键词：

Razumikhin-type theorems; Functional differential inequalities; Stability; Stochastic functional differential equations; TO-STATE STABILITY; TIME-DELAY SYSTEMS; EXPONENTIAL STABILITY; DECAY STABILITY; THEOREMS; STABILIZATION; EQUATIONS; CRITERIA;

D O I：

10.1016/j.cnsns.2020.105253

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper proposes the concept of Razumikhin-type functional differential inequalities and points out that certain quantitative properties can be established for the Razumikhin-type functional differential inequalities. By virtue of certain auxiliary functions, some fundamental results on the quantitative bounds for the Razumikhin-type functional differential inequalities are systemically established in the paper, and these bounds are applied to deduce the basic Razumikhin-type stability theorems, including those for Ito stochastic functional differential equations. Two examples are given to illustrate the application of the established quantitative properties and to verify the effectiveness of our approach. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：13

共 44 条

[21] On an estimate of the decay rate for applications of Razumikhin-type theorems
Hou, CH
Qian, JX
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1998, 43 (07) : 958 - 960
[22] Razumikhin-type Theorems on Exponential Stability of Stochastic Functional Differential Equations with Infinite Delay
Zhihao Yang
Enwen Zhu
Yong Xu
Yimin Tan
Acta Applicandae Mathematicae, 2010, 111 : 219 - 231
[23] Razumikhin-type theorem for pth exponential stability of impulsive stochastic functional differential equations based on vector Lyapunov function
Cao, Wenping
Zhu, Quanxin
NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2021, 39
[24] Razumikhin-type Theorems on Exponential Stability of Stochastic Functional Differential Equations with Infinite Delay
Yang, Zhihao
Zhu, Enwen
Xu, Yong
Tan, Yimin
ACTA APPLICANDAE MATHEMATICAE, 2010, 111 (02) : 219 - 231
[25] Razumikhin method for impulsive functional differential equations of neutral type
Li, Xiaodi
Deng, Feiqi
CHAOS SOLITONS & FRACTALS, 2017, 101 : 41 - 49
[26] Razumikhin-type theorems on pth moment boundedness of neutral stochastic functional differential equations with Makovian switching
Song, Yinfang
Zeng, Zhigang
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2018, 355 (17): : 8296 - 8312
[27] Razumikhin-type theorems for impulsive differential equations with piecewise constant argument of generalized type
Xi, Qiang
ADVANCES IN DIFFERENCE EQUATIONS, 2018,
[28] Razumikhin-type theorem on time-changed stochastic functional differential equations with Markovian switching
Zhang, Xiaozhi
Yuan, Chenggui
OPEN MATHEMATICS, 2019, 17 : 689 - 699
[29] Razumikhin-type theorems for impulsive differential equations with piecewise constant argument of generalized type
Qiang Xi
Advances in Difference Equations, 2018
[30] Razumikhin-type theorems on the moment stability of the exact and numerical solutions for the stochastic pantograph differential equations
Guo, Ping
Li, Chong-Jun
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 355 : 77 - 90

← 1 2 3 4 5 →