Distributed Luenberger Observer Design

This paper presents a distributed design scheme of the Luenberger-type state observer for continuous-time linear dynamical systems. The proposed observer consists of networked local observers, and each local observer computes the estimate by the local measurements, which may not be sufficient to recover the full state. Therefore, by communicating with the neighboring observers, the proposed observer compensates for the insufficient information. The novelty of the proposed method is the design of two observer gains; one for local measurements and the other for the information exchange. By exploring the structure of gain matrices, our design can assign the injection gain only to " detectable" part of the estimate for the local measurements, and for the " undetectable" portion of the estimate, the gain of the information from neighboring observers is set to be relatively higher than others. It turns out that this intuitive idea leads to a simple design of distributed Luenberger-type observers.