  In this paper we consider the distributed estimation problem for
continuous-time linear time-invariant (LTI) systems. A single linear plant is
observed by a network of local observers. Each local observer in the network
has access to only part of the output of the observed system, but can also
receive information on the state estimates of its neigbours. Each local
observer should in this way generate an estimate of the plant state. In this
paper we study the problem of existence of a reduced order distributed
observer. We show that if the observed system is observable and the network
graph is a strongly connected directed graph, then a distributed observer
exists with state space dimension equal to $Nn - \sum_{i =1}^N p_i$, where $N$
is the number of network nodes, $n$ is the state space dimension of the
observed plant, and $p_i$ is the rank of the output matrix of the observed
output received by the $i$th local observer. In the case of a single observer,
this result specializes to the well-known minimal order observer in classical
observer design.
