Security Control for Fuzzy Singularly Perturbation Systems Under DoS Attacks

This study investigates the security control issue for fuzzy singularly perturbed systems (FSPSs) subjected to Denial-of-Service (DoS) attacks. To accurately characterize the dynamics of DoS attacks, an innovative duration-dependent switching rule is proposed, guided by a joint probability distribution function that incorporates both the current attack mode and its dwell time. Unlike traditional Markov/semi-Markov chains, this approach utilizes duration-conditioned sojourn probabilities to eliminate the necessity for explicit transition probabilities estimation, significantly simplifying implementation and reducing computational complexity in multi-mode attack scenarios. Additionally, an attack compensation mechanism explicitly designed to maintain system stability is developed. Furthermore, a non-monotonic Lyapunov function aligned with the proposed switching logic is introduced, resulting in less conservative stability criteria that guarantee the mean-square stability of closed-loop FSPSs. The effectiveness and resilience of the proposed methodology are substantiated through a numerical simulation and a practical case study, highlighting its superior performance in mitigating the adverse effects of DoS attacks compared to existing methodologies. Note to Practitioners—With the continuous advancement in network-based control technologies, singularly perturbed systems have gained significant attention due to their inherent capability to handle dynamics that evolve across multiple time scales. Practical engineering systems frequently encounter uncertainties, including external disturbances, equipment failures, and cyber threats such as Denial-of-Service (DoS) attacks, which can profoundly impact system states and operational stability. Particularly, DoS attacks introduce substantial risks depending on their duration and operational mode. Recognizing these practical concerns, this study proposes an advanced joint probability distribution model that explicitly incorporates both the current attack mode and its duration. By adopting a duration-dependent sojourn probability based on general distributions, the model closely aligns with real-world operational conditions. Additionally, industrial control systems experiencing DoS attacks often face critical information loss, potentially leading to severe instabilities, such as oscillations or divergence. To address these risks, this paper presents a sophisticated gain compensation mechanism designed explicitly for maintaining robust system performance under attack-induced disruptions. This approach ensures that reliable control gains remain available even when essential data is compromised, significantly enhancing system resilience and stability under challenging attack conditions.