Robust Dynamic Output Feedback Control for Uncertain Fast Sampling Discrete-Time Singularly Perturbed Systems

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.