Design of reduced-order multirate input compensators for output injection feedback laws

Output injection feedback is a special kind of pole-positioning mechanism whereby linear combinations of the output measurements are fed directly into the plant's state. Using this mechanism, arbitrary closed-loop pole assignment can be achieved so long as the plant is completely observable. In the event that output injection feedback is not possible, a dual-observer-based compensator can be used to realize the pole-positioning effect of output injection. In this paper, we consider discrete-time systems and derive the equivalent dual-observer-based compensator, herein termed a single-rate input compensator. Further, we explore the concept of multirate input sampling and show that a multirate input compensator (employing multirate sampling of the plant input) of dimension much smaller than that of the single-rate input compensator (employing single-rate input sampling of the plant input) can be designed. Necessary and sufficient conditions for the existence of both types of compensators are found. Design procedures for constructing these compensators are also outlined.