On the time-varying Halanay inequality with applications to stability analysis of time-delay systems

被引：19
作者：
Li, Haifang [1 ]
Zhou, Bin [1 ]
Hou, Mingzhe [1 ]
Duan, Guangren [1 ]
机构：
[1] Harbin Inst Technol, Ctr Control Theory & Guidance Technol, Harbin 150001, Peoples R China
来源：
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS | 2021年 / 358卷 / 10期
关键词：
EXPONENTIAL STABILITY; IMPROVED RAZUMIKHIN; NEURAL-NETWORKS; ASYMPTOTIC STABILITY; JUMPING SYSTEMS; DISSIPATIVITY;
D O I：
10.1016/j.jfranklin.2021.04.046
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The main results of the paper are improvements on the stability analysis of Halanay inequalities with time-varying coefficients in both continuous-time and discrete-time setting. Three classes of improved conditions are established to ensure that the solution to the Halanay inequality is uniformly exponentially stable. The merit of the proposed new conditions is that the coefficients of the Halanay inequality can be unbounded and sign indefinite. This is achieved by using the notion and properties of uniformly asymptotic stable (UAS) functions. Based on the improved stability conditions for the Halanay inequality and the Lyapunov Razumikhin approach, three classes of sufficient conditions are established for testing the stability of time-varying time-delay systems. Finally, the advantages of the proposed methods are illustrated by some numerical examples with some of them borrowed from the literature. (C) 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
引用
收藏
页码：5488 / 5512
页数：25
相关论文
共 43 条
  • [1] Agarwal R.P., 1997, Advanced Topics in Difference Equations
  • [2] Agarwal R. P., 1993, DIFFERENCE EQUATIONS
  • [3] [Anonymous], 1969, Differential and Integral Inequalities: Theory and Applications: Volume I: Ordinary Differential Equations
  • [4] Baker C.T.H., 2000, VOLTERRA EQUATIONS A, P39
  • [5] Exponential stability in mean square of impulsive stochastic difference equations with continuous time
    Bao, Jianhai
    Hou, Zhenting
    Wang, Fuxing
    [J]. APPLIED MATHEMATICS LETTERS, 2009, 22 (05) : 749 - 753
  • [6] l2 gain analysis and state feedback stabilization of switched systems with multiple additive time-varying delays
    Chen, Guoliang
    Xia, Jianwei
    Zhuang, Guangming
    Zhang, Baoyong
    [J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2017, 354 (16): : 7326 - 7345
  • [7] Halanay A., 1966, Differential Equations: Stability, Oscillations, TimeLags
  • [8] Improved stability conditions of time-varying delay systems based on new Lyapunov functionals
    Lee, Tae H.
    Park, Ju H.
    [J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2018, 355 (03): : 1176 - 1191
  • [9] Global Dissipativity of Inertial Neural Networks with Proportional Delay via New Generalized Halanay Inequalities
    Li, Hongfei
    Li, Chuandong
    Zhang, Wei
    Xu, Jing
    [J]. NEURAL PROCESSING LETTERS, 2018, 48 (03) : 1543 - 1561
  • [10] A sampled-data approach to distributed H∞ resilient state estimation for a class of nonlinear time-delay systems over sensor networks
    Li, Qi
    Shen, Bo
    Wang, Zidong
    Alsaadi, Fuad E.
    [J]. JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2017, 354 (15): : 7139 - 7157
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