Fractional-Order Sliding Mode Control for Hidden Semi-Markov Jump Systems Under DoS Attacks and Uncertain Emission Probabilities

This paper addresses the stability analysis and control design for discrete-time hidden semi-Markov jump systems under the compounded challenges of denial-of-service (DoS) attacks and incomplete emission probabilities. Such conditions are prevalent in modern networked control systems, yet they pose significant hurdles for robust controller design. Existing control methods, typically based on integer-order dynamics, are inherently memoryless, struggling to effectively mitigate the long-term impact of mode observation uncertainties and intermittent cyberattacks. To overcome these challenges, we propose, for the first time, a fractional-order sliding mode control (FOSMC) strategy tailored for this class of systems. The core of our method is a novel sliding surface that leverages a discrete fractional-order sum to embed the system’s history—including observed modes and elapsed sojourn times—into the control logic. This memory-based approach enhances robustness against both mode observation uncertainties and adversarial packet losses. A corresponding FOSMC law is synthesized to ensure finite-time reachability of this surface. We derive sufficient conditions, formulated as linear matrix inequalities, to guarantee the mean-square stability of the resulting sliding mode dynamics.A numerical simulation validates the effectiveness of the proposed control scheme, demonstrating a convergence speed improvement ranging from 40% (under moderate attacks) to nearly 50% (under severe attacks) over its integer-order counterpart, conclusively validating its performance enhancement capability under compound uncertainties.