Robust fault detection filter design for uncertain neutral systems with time delays: A case study of two-stage recycle reactors

² Control and Instrumentation Engineering Department, College of Engineering and Physics, King Fahd University of Petroleum & Minerals, Dhahran, Eastern Province, Saudi Arabia

³ Interdisciplinary Research Center for Smart Mobility and Logistics, King Fahd University of Petroleum & Minerals, Dhahran, Eastern Province, Saudi Arabia

⁴ Department of Automatic and Electrical Engineering, National Engineering School of Gabes, University of Gabes, Gabes, Tunisia

⁵ LaPhyMNE Laboratory (LR05ES14), FSG, University of Gabes, Gabes, Tunisia

†These authors contributed equally to this work.

IJOCTA, 026150059 https://doi.org/10.36922/IJOCTA026150059

Received: 8 April 2026 | Revised: 8 June 2026 | Accepted: 15 June 2026 | Published online: 6 July 2026

© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )

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Abstract

This study introduces a robust fault detection filter (RFDF) for uncertain neutral-type systems with time delays in both state variables and their derivatives. Such systems are frequently encountered in manufacturing processes, where delays and parametric uncertainties can significantly impact system reliability and efficiency. The proposed method addresses the simultaneous challenges presented by unknown inputs and parameter uncertainties. A Lyapunov–Krasovskii functional is employed to derive sufficient conditions for ensuring the asymptotic stability of the estimation error dynamics. The design problem is formulated as a convex optimization problem solved via linear matrix inequalities. A new fault detection scheme has been developed comprising three key components: a model-based fault detection filter, a reference residual generator operating under nominal conditions, and a resilient residual generator that is impervious to disturbances yet responsive to faults. An H∞ optimization criterion is applied to maximize fault sensitivity while minimizing the effect of unknown disturbances. The effectiveness of the proposed RFDF is validated through simulation of a two-stage chemical reactor system subject to neutral time delays and recycle streams. The results demonstrate the proposed filter’s ability to detect actuator and sensor faults under uncertain conditions, confirming its robustness and effectiveness.

Keywords

Neutral time-delay system

Parameter uncertainties

Robust fault detection filter

Lyapunov–Krasovskii functional

Linear matrix inequality H∞

Optimization

Funding

None.

Conflict of interest

The authors have no relevant financial or nonfinancial interests to disclose.

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