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Stability analysis and applications of time-delay systems subject to delayed impulses
Xiaoying Chen1, Liujuan Chen2, Junyan Xu3
1Department of Mathematics Research, Fujian Institute of Education, Fuzhou 350001, China; School of Computer Science and Technology, Zhejiang Normal University, Jinhua 321004, China.
ISA Transactions
|September 27, 2025
Summary
This study ensures exponential stability in nonlinear time-delay systems with delayed impulses, even with arbitrary delay durations. The findings enhance control strategies for complex systems like sewage treatment and Chua
Area of Science:
- Control Theory
- Nonlinear Dynamics
- Systems Engineering
Background:
- Nonlinear time-delay systems are crucial in many engineering applications.
- Impulsive control and perturbations introduce stability challenges.
- Existing methods often restrict time-delay parameters.
Purpose of the Study:
- To investigate the stability of nonlinear time-delay systems under delayed impulses.
- To analyze the impact of delayed impulsive control and perturbations.
- To develop new criteria for ensuring exponential stability.
Main Methods:
- Utilizing Halanay-type inequality techniques.
- Developing sufficient criteria for exponential stability.
- Analyzing systems with time-varying delays and delayed impulses.
Main Results:
- Established sufficient criteria for exponential stability.
- Removed restrictions on relative time-delay sizes.
- Demonstrated that finite or exceeding impulse interval delays do not compromise stability, only convergence rate.
Conclusions:
- The derived criteria effectively ensure exponential stability for nonlinear time-delay systems with delayed impulses.
- The results offer more flexibility in designing impulsive control strategies.
- Theoretical findings are validated through applications in sewage treatment and Chua's circuits synchronization.
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