Observer-based controller design for nonstandard singularly perturbed sampled data systems

A linear shift-invariant singularly perturbed sampled-data system is considered with the assumption that not all states are available for measurement, and therefore the design is in the form of an observer-based controller. Given the two-time-scale property of the system, singular perturbation theory may be used to design lower-order feedback controllers for the slow and fast subsystems. It is assumed that the system is in the form of a singularly perturbed nonstandard model. Prefeedback control of the fast states is utilized to put the system into a standard form prior to the slow and fast decomposition of the full system. The problem of an observer-based controller is then addressed. Assuming that the slow states are not available for direct measurement, state feedback gain and observer gain were designed for the reduced-order subsystem. The composition of these controllers is shown to stabilize the closed-loop system