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Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
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Input-delayed time/event-triggered intermittent control for incremental stability.

Ping Li1, Bin Liu2, Ming-Han Jiang2

  • 1School of Mathematics, Southwest Minzu University, Chengdu, 610041, China.

ISA Transactions
|April 26, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces event-triggered intermittent control (ETIC) for enhanced incremental stability in dynamical systems. ETIC with multiple check-periods achieves minimal activation time rates, outperforming other control methods, especially with input delays.

Keywords:
ContractionEvent-triggered intermittent control (ETIC)Incremental stabilityInput delayMinimal activation time rateTime-triggered intermittent control (TTIC)

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Area of Science:

  • Control Theory
  • Dynamical Systems Analysis
  • Stability Theory

Background:

  • Continuous dynamical systems require robust control strategies for stability.
  • Intermittent control offers efficiency but faces challenges with input delays and stability guarantees.
  • Incremental stability is crucial for analyzing system behavior under perturbations.

Purpose of the Study:

  • To investigate incremental stability of continuous dynamical systems using input-delayed time/event-triggered intermittent control.
  • To propose and analyze novel event-triggered intermittent control (ETIC) strategies.
  • To compare the performance of different intermittent control methods regarding delay-dependent minimal activation time rate (D-MATR).

Main Methods:

  • Formulation of incremental stability via input-delayed intermittent control as a delay-dependent minimal activation time rate (D-MATR) problem.
  • Derivation of criteria for incremental global exponential stability (δGES) using time-triggered intermittent control (TTIC).
  • Proposal and algorithmic development of event-triggered intermittent control (ETIC) with single and multiple check-periods, including sampling-based approaches.

Main Results:

  • The proposed ETIC with multiple check-periods demonstrates a superior ability to achieve the minimal activation time rate for δGES compared to TTIC and other intermittent controls.
  • A larger input delay was found to necessitate a larger D-MATR for achieving δGES.
  • Theoretical derivations and numerical simulations validated the effectiveness of the proposed methods.

Conclusions:

  • Event-triggered intermittent control, particularly with multiple check-periods, offers an effective strategy for enhancing incremental stability in the presence of input delays.
  • The developed methods provide a theoretical framework and practical algorithms for designing stable and efficient intermittent control systems.
  • Applications in target tracking and missile dynamics consistency highlight the practical utility of the proposed TTIC and ETIC strategies.