Review of stability and stabilization for impulsive delayed systems

Xueyan Yang; Xiaodi Li; Qiang Xi; Peiyong Duan; Xueyan Yang; Xiaodi Li; Qiang Xi; Peiyong Duan

doi:10.3934/mbe.2018069

Mathematical Biosciences and Engineering

2018, Volume 15, Issue 6: 1495-1515. doi: 10.3934/mbe.2018069

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Review of stability and stabilization for impulsive delayed systems

Xueyan Yang ^{1
,},
Xiaodi Li ^{1,2
,
,},
Qiang Xi ^{3
,},
Peiyong Duan ^{1,2
,}

1.
School of Mathematics and Statistics, Shandong Normal University, Ji'nan 250014, China
2.
Shandong Province Key Laboratory of Medical Physics and Image Processing Technology, Shandong Normal University, Ji'nan 250014, China
3.
School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Ji'nan 250014, China

Received: 03 August 2018 Revised: 19 August 2018 Published: 01 December 2018
MSC : Primary: 58F15, 58F17; Secondary: 53C35

This paper reviews some recent works on impulsive delayed systems (IDSs). The prime focus is the fundamental results and recent progress in theory and applications. After reviewing the relative literatures, this paper provides a comprehensive and intuitive overview of IDSs. Five aspects of IDSs are surveyed including basic theory, stability analysis, impulsive control, impulsive perturbation, and delayed impulses. Then the research prospect is given, which provides a reference for further study of IDSs theory.
- Impulsive delayed systems,
- stability analysis,
- impulsive control,
- impulsive perturbation,
- delayed impulses
Citation: Xueyan Yang, Xiaodi Li, Qiang Xi, Peiyong Duan. Review of stability and stabilization for impulsive delayed systems[J]. Mathematical Biosciences and Engineering, 2018, 15(6): 1495-1515. doi: 10.3934/mbe.2018069

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Abstract

This paper reviews some recent works on impulsive delayed systems (IDSs). The prime focus is the fundamental results and recent progress in theory and applications. After reviewing the relative literatures, this paper provides a comprehensive and intuitive overview of IDSs. Five aspects of IDSs are surveyed including basic theory, stability analysis, impulsive control, impulsive perturbation, and delayed impulses. Then the research prospect is given, which provides a reference for further study of IDSs theory.

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