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 observerbased 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, To.
1. Inrroduction
It is well-known that simple (low-order) linear compensators are normally to be preferred to complex (high-order) linear compensators for finite-dimensional linear time-invariant (FDLTI) plants. Reasons for this include the higher reliability associated with lower complexity in the hardware, the lesser complexity in the software, and higher computational efficiency associated with the reduced computational burden. Simple compensators are likely to be easier to understand at a conceptual level so that they are more likely to be accepted by design engineers and managers. Accordingly, there is a desire to have methods available to design a low-order compensator for a higher-order plant.
The search for reduced-order observer-based and nonobserver-based compensator designs has been an ongoing process (see Luenberger, 1966, Tse andAthans, 1970;Fortmann and Williamson, 1972;Murdoch, 1973; Hagiwara et al., W90). Controllers which do not employ observers but employ multirate sampling of the plant output were studied *