On the cooperative observability of a continuous-time linear system on an undirected network

In traditional control theory, a single observer has access all the measured outputs of the plant to estimates its asymptotically. In many real world engineering systems, it may be difficult to build a single observer that has access to all the measured outputs. One way around this difficulty is to build a network of cooperative observers, each of which obtains a portion of the measurement outputs, that collectively produce an asymptotic estimate of the plant state. In this paper, we construct a network of such observers for a continuous-time linear system. Assuming that these observers are connected through an undirected connected network, we establish a necessary and sufficient condition on the plant parameters under which the network of observers will achieve asymptotic omniscience. A network of cooperative observers is said to achieve asymptotic omniscience if their states all converge to the plant state asymptotically. Numerical simulation results are presented to validate theoretical results. The design of cooperative observers sheds some light on the solution of some other real-world problems, such as the design of networked location-based services and sensor networks.