Continuous approximation of linear impulsive systems and a new form of robust stability

被引：1

作者：

Church, Kevin E. M. ^{[1
]}

Smith, Robert ^{[2
]}

机构：

[1] Univ Waterloo, Dept Appl Math, Waterloo, ON, Canada

[2] Univ Ottawa, Dept Math & Stat, Ottawa, ON, Canada

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 457卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Impulsive differential equations; Impulse extension; Stability; Robust stability; Time-scale tolerance; Exponential regulator; PSEUDOSPECTRAL RADIUS; VACCINATION; ALGORITHMS; DYNAMICS;

D O I：

10.1016/j.jmaa.2017.08.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The time-scale tolerance for linear ordinary impulsive differential equations is introduced. How large the time-scale tolerance is directly reflects the degree to which the qualitative dynamics of the linear impulsive system can be affected by replacing the impulse effect with a continuous (as opposed to discontinuous, impulsive) perturbation, producing what is known as an impulse extension equation. Theoretical properties related to the existence of the time-scale tolerance are given for periodic systems, as are algorithms to compute them. Some methods are presented for general, aperiodic systems. Additionally, sufficient conditions for the convergence of solutions of impulse extension equations to the solutions of their associated impulsive differential equation are proven. Counterexamples are provided. (c) 2017 Elsevier Inc. All rights reserved.

引用

页码：616 / 644

页数：29

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