Robustness for Non-instantaneous Impulsive Equations via Quadratic Lyapunov Functions

Mengmeng Li; Jin Rong Wang; Donal O’Regan

doi:10.1007/s40840-022-01336-7

Robustness for Non-instantaneous Impulsive Equations via Quadratic Lyapunov Functions

Mengmeng Li
, Jin Rong Wang
, Donal O’Regan

Mathematics

Guizhou University

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

2 Citations (Scopus)

Abstract

In this paper, we introduce an impulsive evolution operator and Lyapunov functions for a linear system and obtain relations between them under suitable conditions. Those relations are used to investigate nonuniform exponential contraction behavior which is an important tool for dealing with nonuniform exponential stability of the dynamics. As an application, we give the condition of the existence of nonuniform exponential contraction behavior of linear perturbed systems under sufficiently small linear perturbations.

Original language	English
Pages (from-to)	2053-2070
Number of pages	18
Journal	Bulletin of the Malaysian Mathematical Sciences Society
Volume	45
Issue number	5
DOIs	https://doi.org/10.1007/s40840-022-01336-7
Publication status	Published - Sept 2022

Keywords

Lyapunov functions
Non-instantaneous impulsive equations
Nonuniform hyperbolicity
Robustness

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10.1007/s40840-022-01336-7

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title = "Robustness for Non-instantaneous Impulsive Equations via Quadratic Lyapunov Functions",

abstract = "In this paper, we introduce an impulsive evolution operator and Lyapunov functions for a linear system and obtain relations between them under suitable conditions. Those relations are used to investigate nonuniform exponential contraction behavior which is an important tool for dealing with nonuniform exponential stability of the dynamics. As an application, we give the condition of the existence of nonuniform exponential contraction behavior of linear perturbed systems under sufficiently small linear perturbations.",

keywords = "Lyapunov functions, Non-instantaneous impulsive equations, Nonuniform hyperbolicity, Robustness",

author = "Mengmeng Li and Wang, \{Jin Rong\} and Donal O{\textquoteright}Regan",

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AU - Li, Mengmeng

AU - Wang, Jin Rong

AU - O’Regan, Donal

PY - 2022/9

Y1 - 2022/9

N2 - In this paper, we introduce an impulsive evolution operator and Lyapunov functions for a linear system and obtain relations between them under suitable conditions. Those relations are used to investigate nonuniform exponential contraction behavior which is an important tool for dealing with nonuniform exponential stability of the dynamics. As an application, we give the condition of the existence of nonuniform exponential contraction behavior of linear perturbed systems under sufficiently small linear perturbations.

AB - In this paper, we introduce an impulsive evolution operator and Lyapunov functions for a linear system and obtain relations between them under suitable conditions. Those relations are used to investigate nonuniform exponential contraction behavior which is an important tool for dealing with nonuniform exponential stability of the dynamics. As an application, we give the condition of the existence of nonuniform exponential contraction behavior of linear perturbed systems under sufficiently small linear perturbations.

KW - Lyapunov functions

KW - Non-instantaneous impulsive equations

KW - Nonuniform hyperbolicity

KW - Robustness

UR - https://www.scopus.com/pages/publications/85133166843

U2 - 10.1007/s40840-022-01336-7

DO - 10.1007/s40840-022-01336-7

M3 - Article

AN - SCOPUS:85133166843

SN - 0126-6705

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SP - 2053

EP - 2070

JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

IS - 5

ER -

Robustness for Non-instantaneous Impulsive Equations via Quadratic Lyapunov Functions

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Keywords

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