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Robust Stabilization of Linear Time-Delay Systems under Denial-of-Service Attacks.

Abdul-Wahid A Saif1,2, Sami El-Ferik1,2, Siddig M Elkhider1

  • 1Interdisciplinary Center of Smart Mobility and Logistics, King Fahd University of Petroleum and Minerals, P.O. Box 5067, Dhahran 31261, Saudi Arabia.

Sensors (Basel, Switzerland)
|July 14, 2023
PubMed
Summary

This study introduces a novel PID state feedback strategy to stabilize linear time-delay systems against denial-of-service (DoS) attacks. New linear matrix inequalities (LMIs) ensure robust system stabilization under various time-delay conditions.

Keywords:
DoS attacksLMI approachPID-like state feedback controlrobust controltime-delay systems

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Area of Science:

  • Control Systems Engineering
  • Cybersecurity
  • Applied Mathematics

Background:

  • Linear time-delay systems are vulnerable to denial-of-service (DoS) attacks, which can manifest as delay-independent or delay-dependent behaviors.
  • Traditional proportional-integral-derivative (PID) controllers act on error signals, which may be insufficient for robust stabilization under attack conditions.

Purpose of the Study:

  • To develop and analyze a new PID state feedback control strategy for stabilizing linear time-delay systems under DoS attacks.
  • To address both continuous bounded and differentiable time-varying delay scenarios.
  • To ensure robust system stabilization against sophisticated cyber threats.

Main Methods:

  • Utilizing the Lyapunov-Krasovskii functional (LKF) to formulate new linear matrix inequalities (LMIs).
  • Designing PID-like state feedback gains based on the derived LMIs.
  • Analyzing system stability under two distinct time-delay models.

Main Results:

  • New LMIs were successfully derived for robust stabilization.
  • The proposed PID state feedback strategy effectively ensures system stability.
  • The effectiveness of the method was demonstrated through numerical examples.

Conclusions:

  • The developed PID state feedback strategy offers a robust solution for stabilizing linear time-delay systems against DoS attacks.
  • The LKF-based LMI approach provides a systematic way to compute stabilizing gains.
  • This research contributes to enhancing the resilience of critical systems in adversarial environments.