  We study the problem of designing distributed functional observers for LTI
systems. Specifically, we consider a setting consisting of a state vector that
evolves over time according to a dynamical process. A set of nodes distributed
over a communication network wish to collaboratively estimate certain functions
of the state. We first show that classical existence conditions for the design
of centralized functional observers do not directly translate to the
distributed setting, due to the coupling that exists between the dynamics of
the functions of interest and the diverse measurements at the various nodes.
Accordingly, we design transformations that reveal such couplings and identify
portions of the corresponding dynamics that are locally detectable at each
sensor node. We provide sufficient conditions on the network, along with state
estimate update and exchange rules for each node, that guarantee asymptotic
reconstruction of the functions at each sensor node.
