  We develop a decentralized $H_\infty$ synthesis approach to detection of
biasing misappropriation attacks on distributed observers. Its starting point
is to equip the observer with an attack model which is then used in the design
of attack detectors. A two-step design procedure is proposed. First, an initial
centralized setup is carried out which enables each node to compute the
parameters of its attack detector online in a decentralized manner, without
interacting with other nodes. Each such detector is designed using the
$H_\infty$ approach. Next, the attack detectors are embedded into the network,
which allows them to detect misappropriated nodes from innovation in the
network interconnections.
