Robust Disturbance Attenuation with Stability for Discrete-Time Singularly Perturbed Systems with Nonlinear Disturbances

This article delves into the robust disturbance attenuation and stability of discrete-time singularly perturbed systems (DTSPSs) with nonlinear disturbances, a critical area in control theory. The study introduces a novel framework that combines time-scale decomposition with Linear Matrix Inequality (LMI) techniques to address the challenges posed by high dimensionality and numerical stiffness. Unlike existing methods, this approach does not require pre-determined upper bounds for the perturbation parameter, thereby reducing conservatism and enhancing practical applicability. The article provides a unified LMI-based condition for full-order systems, ensuring both standard and H∞ performance. It also presents a systematic method for designing feedback control, which naturally decomposes into slow and fast subsystem controller designs, leading to more efficient implementations. The effectiveness of the proposed method is demonstrated through detailed numerical examples, showcasing its ability to achieve larger upper bounds for the perturbation parameter and effective disturbance attenuation. The study concludes with a discussion on future work, focusing on addressing computational complexity and optimal gain selection.