This paper considers the dynamic output feedback (DOF) control problems for a class of uncertain discrete-time singularly perturbed systems by using reduced-order subsystems (ROSs). A sufficient condition in terms of a linear matrix inequality (LMI) is provided to guarantee the existence of the DOF controller of the ROSs. The corresponding controller gain matrices can be solved by the proposed LMIs. The results show that the DOF controller that is designed for the ROSs can stabilize the original full-order system (FOS) when the perturbation parameter is sufficiently small, although there are system uncertainties. Thus, the presented DOF controller guarantees that the FOS is robust not only for the singular perturbation parameter but also for the system uncertainties. Furthermore, we also explicitly show that this case fails when using static output feedback. That is, a static output feedback controller can always be found to stabilize the ROSs, but it destabilizes the FOSs. Finally, an experimental example for the nuclear reactor model is employed to illustrate the validity and feasibility of the developed methods.

中文翻译：

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不确定快速采样离散时间奇异摄动系统的鲁棒动态输出反馈控制

本文通过使用降阶子系统（ROS）来考虑一类不确定离散时间奇异摄动系统的动态输出反馈（DOF）控制问题。提供了线性矩阵不等式 (LMI) 方面的充分条件来保证 ROS 的 DOF 控制器的存在。相应的控制器增益矩阵可以通过建议的 LMI 求解。结果表明，当扰动参数足够小时，为ROS设计的自由度控制器可以稳定原始全阶系统（FOS），尽管存在系统不确定性。因此，所提出的自由度控制器保证了 FOS 不仅对于奇异扰动参数而且对于系统不确定性都是鲁棒的。此外，我们还明确表明，当使用静态输出反馈时，这种情况会失败。也就是说，总是可以找到一个静态输出反馈控制器来稳定 ROS，但它会破坏 FOS。最后，通过核反应堆模型的实验实例来说明所开发方法的有效性和可行性。