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

[31] Razumikhin-type technique on stability of exact and numerical solutions for the nonlinear stochastic pantograph differential equations
Guo, Ping
Li, Chong-Jun
BIT NUMERICAL MATHEMATICS, 2019, 59 (01) : 77 - 96
[32] The Razumikhin approach on general decay stability for neutral stochastic functional differential equations
Pavlovic, Gorica
Jankovic, Svetlana
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2013, 350 (08): : 2124 - 2145
[33] RAZUMIKHIN-TYPE THEOREMS ON MOMENT EXPONENTIAL STABILITY OF FUNCTIONAL DIFFERENTIAL EQUATIONS INVOLVING TWO-TIME-SCALE MARKOVIAN SWITCHING
Wu, Fuke
Yin, George
Wang, Le Yi
MATHEMATICAL CONTROL AND RELATED FIELDS, 2015, 5 (03) : 697 - 719
[34] Razumikhin-Type Theorems on pth Moment Exponential Stability of Impulsive Stochastic Delay Differential Equations
Peng, Shiguo
Zhang, Yun
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2010, 55 (08) : 1917 - 1922
[35] Razumikhin type stability theorems for impulsive functional differential equations
Shen, JH
Yan, JR
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1998, 33 (05) : 519 - 531
[36] New Razumikhin type theorems for impulsive functional differential equations
Luo, ZG
Shen, JH
APPLIED MATHEMATICS AND COMPUTATION, 2002, 125 (2-3) : 375 - 386
[37] The improvement of Razumikhin type theorems for impulsive functional differential equations
Liu, Kaien
Yang, Guowei
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (09) : 3104 - 3109
[38] NEW RAZUMIKHIN TYPE STABILITY THEOREM FOR IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS
Wang, Jiayu
Li, Xiaodi
ANALYSIS AND APPLICATIONS, 2011, 9 (03) : 315 - 327
[39] THE RAZUMIKHIN TYPE THEOREMS OF STABILITY AND BOUNDEDNESS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY
陈强
陈海明
Annals of Applied Mathematics, 1997, (01) : 19 - 22
[40] Lyapunov-Razumikhin method for impulsive functional differential equations and applications to the population dynamics
Stamova, IM
Stamov, GT
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 130 (1-2) : 163 - 171

← 1 2 3 4 5 →