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Volume 14
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Article

An Event-Triggered Observer-Based Control Approach for Enhancing Resilience of Cyber–Physical Systems Under Markovian Cyberattacks

by
Eya Hassine
1,2,†,
Assem Thabet
1,†,
Noussaiba Gasmi
2,*,† and
Ghazi Bel Haj Frej
3,†
1
Research Lab. MACS, University of Gabes, Gabes 6072, Tunisia
2
Laboratoire d’Informatique et Telecommunications, ECAM Louis de Broglie, 35170 Bruz, France
3
IMS Laboratory, Centre National de la Recherche Scientifique–Unité Mixte de Recherche 5218, Bordeaux Institut Polytechnique, University of Bordeaux, 33405 Bordeaux, France
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Actuators 2025, 14(8), 412; https://doi.org/10.3390/act14080412
Submission received: 7 July 2025 / Revised: 10 August 2025 / Accepted: 18 August 2025 / Published: 21 August 2025
(This article belongs to the Special Issue Actuator Technologies and Control: Materials, Devices and Applications)
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Abstract

This paper presents a resilient observer-based and event-triggered control scheme for discrete-time Cyber–Physical Systems (CPS) under Markovian Cyber-Attacks (MCA). The proposed framework integrates a Luenberger observer for cyberattack detection with a state-feedback controller designed to preserve system stability in the presence of Denial-of-Service (DoS) and False Data Injection (FDI) attacks. Attack detection is achieved through residual signal generation combined with Markovian modeling of the attack dynamics. System stability is guaranteed by formulating relaxed Linear Matrix Inequality (LMI) conditions that incorporate relaxation variables, a diagonal Lyapunov function, the S-procedure, and congruence transformations. Moreover, the Event-Triggered Mechanism (ETM) efficiently reduces communication load without degrading control performance. Numerical simulations conducted on a three-tank system benchmark confirm enhanced detection accuracy, faster recovery, and strong robustness against uncertainties.
Keywords: cyber–physical systems (CPS); Luenberger observer; state-feedback control; denial-of-service (DoS); false data injection (FDI); Markovian cyberattack; linear matrix inequality (LMI); Lyapunov function; S-procedure cyber–physical systems (CPS); Luenberger observer; state-feedback control; denial-of-service (DoS); false data injection (FDI); Markovian cyberattack; linear matrix inequality (LMI); Lyapunov function; S-procedure

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MDPI and ACS Style

Hassine, E.; Thabet, A.; Gasmi, N.; Bel Haj Frej, G. An Event-Triggered Observer-Based Control Approach for Enhancing Resilience of Cyber–Physical Systems Under Markovian Cyberattacks. Actuators 2025, 14, 412. https://doi.org/10.3390/act14080412

AMA Style

Hassine E, Thabet A, Gasmi N, Bel Haj Frej G. An Event-Triggered Observer-Based Control Approach for Enhancing Resilience of Cyber–Physical Systems Under Markovian Cyberattacks. Actuators. 2025; 14(8):412. https://doi.org/10.3390/act14080412

Chicago/Turabian Style

Hassine, Eya, Assem Thabet, Noussaiba Gasmi, and Ghazi Bel Haj Frej. 2025. "An Event-Triggered Observer-Based Control Approach for Enhancing Resilience of Cyber–Physical Systems Under Markovian Cyberattacks" Actuators 14, no. 8: 412. https://doi.org/10.3390/act14080412

APA Style

Hassine, E., Thabet, A., Gasmi, N., & Bel Haj Frej, G. (2025). An Event-Triggered Observer-Based Control Approach for Enhancing Resilience of Cyber–Physical Systems Under Markovian Cyberattacks. Actuators, 14(8), 412. https://doi.org/10.3390/act14080412

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