Dynamic output feedback control for fast sampling discrete-time singularly perturbed systems

This study is concerned with the dynamic output feedback control problem for fast sampling discrete-time singularly perturbed systems using the singular perturbation approach. Sufficient conditions in terms of linear matrix inequalities (LMIs) are presented to guarantee the existence of a dynamic output feedback controller for the corresponding slow and fast subsystems, respectively. The controller gains and the corresponding coefficient matrices can be obtained via solving the proposed LMIs. Thus, not only the high dimensionality and the ill condition are alleviated, but also the regularity restrictions attached to the Riccati-based solutions are avoided. The theoretical result demonstrates that the composite dynamic output feedback control designed through those of the slow and fast subsystems can stabilise the full-order discrete-time singularly perturbed systems. Finally, two real world practical examples are provided to show the effectiveness of the obtained results.