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Related Experiment Video

Updated: Sep 9, 2025

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Stability of delayed systems: delay-compensatory impulsive control.

Lian Chen1, Cui Cai1, Song Ling2

  • 1Research Institute of Highway Ministry of Transport, Xitucheng Road No. 8, HaiDian District, Beijing, 100083, China.

ISA Transactions
|August 29, 2025
PubMed
Summary

This study introduces delay-compensatory impulsive control to stabilize systems with unstable dynamics and impulse gains. The research demonstrates that impulse delays can effectively mitigate instability in controlled dynamic systems.

Keywords:
Delay-compensatory impulsive controlDelayed systemHalanay inequalityImpulse delayImpulsive system

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Dynamics
  • Systems Theory

Background:

  • Systems with delayed dynamics and unstable impulse gains present significant control challenges.
  • Existing control methods struggle to effectively manage the destabilizing effects of unstable impulse gains in delayed systems.

Purpose of the Study:

  • To introduce and investigate a novel control strategy, delay-compensatory impulsive control, for stabilizing dynamic systems.
  • To develop a method that utilizes impulse delays to counteract instability caused by unstable impulse gains.
  • To establish conditions for exponential stability in delayed impulse systems.

Main Methods:

  • Formulation of a compensation criterion considering both unstable impulse gains and impulse delays.
  • Proposal of a modified Halanay impulsive delay inequality with real impulse gain.
  • Establishment of sufficient conditions for exponential stability using the compensation criterion and a relaxed Halanay inequality.

Main Results:

  • The proposed delay-compensatory impulsive control strategy effectively counteracts instability from unstable impulse gains.
  • Sufficient conditions for achieving exponential stability in delayed impulse systems were derived.
  • Comparative simulations validated the superiority of the proposed control algorithm.

Conclusions:

  • Delay-compensatory impulsive control is a viable strategy for stabilizing complex dynamic systems.
  • Impulse delays can be strategically employed to mitigate the negative impacts of unstable impulse gains.
  • The findings offer a new approach to enhance the stability of controlled dynamic systems.