Data-Driven Control Methods for Linear Discrete-Time Singularly Perturbed Systems

This paper presents a synergistic control strategy for discrete-time singularly perturbed systems, where data-driven learning is seamlessly combined with LMI-based synthesis. The proposed method fully leverages data collected from system operation or experiments to establish the input–output relationship for controller parameter identification, thereby enabling controller design without requiring an exact mathematical model of the system. First, the influence mechanism of the singular perturbation parameter on system dynamics is analyzed, which reveals the coupling between the fast and slow subsystems and their respective effects on system stability and response speed. Second, without requiring a complete parametric model of the system, valid matrix inequality conditions are constructed based on input–output data for both controller synthesis and singular perturbation parameter estimation. This approach effectively avoids over-reliance on an accurate system model, thus enhancing the feasibility and practical applicability of the proposed method. Lastly, numerous simulation runs are executed to assess the performance of the presented strategy. The results demonstrate that the method not only ensures the global stability of the system across a wide range of singular perturbation parameter values but also achieves excellent performance in terms of convergence speed, robustness and control accuracy, thus offering an effective new approach for controlling discrete-time singularly perturbed systems in complex engineering environments.