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Review of stability and stabilization for impulsive delayed systems
Xueyan Yang1, Xiaodi Li, Qiang Xi
1School of Mathematics and Statistics, Shandong Normal University, Ji'nan 250014, China.
Mathematical Biosciences and Engineering : MBE
|November 13, 2018
Summary
This review covers recent advancements in impulsive delayed systems (IDSs), focusing on fundamental theory and applications. It offers a comprehensive overview of IDSs, including stability, control, and perturbation aspects.
Area of Science:
- Mathematics
- Control Theory
- Dynamical Systems
Background:
- Impulsive delayed systems (IDSs) are a class of dynamical systems with unique characteristics.
- Recent literature has shown significant progress in understanding and applying IDSs.
- A comprehensive review is needed to consolidate current knowledge.
Purpose of the Study:
- To provide a comprehensive and intuitive overview of recent works on impulsive delayed systems (IDSs).
- To survey fundamental results and recent progress in the theory and applications of IDSs.
- To offer insights into future research directions for IDSs theory.
Main Methods:
- Literature review of recent works on IDSs.
- Systematic survey of five key aspects: basic theory, stability analysis, impulsive control, impulsive perturbation, and delayed impulses.
- Analysis of current research trends and prospects.
Main Results:
- A consolidated overview of the fundamental theory of IDSs.
- Summary of recent progress in stability analysis and control strategies for IDSs.
- Discussion on the impact of impulsive perturbation and delayed impulses in system dynamics.
Conclusions:
- The paper provides a valuable reference for researchers in the field of IDSs.
- Identified research prospects offer guidance for future investigations in IDSs theory.
- The review highlights the growing importance and diverse applications of IDSs.
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