Design of reduced-order multirate output linear functional observer-based compensators

Often in control system design, it is only necessary to estimate a single (but prespecified) linear function of the system's state for the purpose of implementing a feedback control law. This can be achieved by a linear functional observer which may have order one less than the observability index of the plant, but generically cannot have smaller order. In this paper, we explore the concept of multirate output sampling and show that a linear functional observer-based compensator employing multirate sampling of the plant output can be designed with dimension much smaller than that of the linear functional observer-based compensator employing single-rate sampling of the plant output. Necessary and sufficient conditions for the existence of the single-rate and multirate output linear functional observer-based compensators are found. Design procedures for constructing these observer-based compensators are also outlined. Furthermore, both types of compensators are strictly causal and open-loop stable for sufficiently small frame period, T₀.