  This paper proposes a novel distributed interval-valued simultaneous state
and input observer for linear time-invariant (LTI) systems that are subject to
attacks or unknown inputs injected both on their sensors and actuators. Each
agent in the network leverages a singular value decomposition (SVD) based
transformation to decompose its observations into two components, one of them
unaffected by the attack signal, which helps to obtain local interval estimates
of the state and unknown input and then uses intersection to compute the best
interval estimate among neighboring nodes. We show that the computed intervals
are guaranteed to contain the true state and input trajectories, and we provide
conditions under which the observer is stable. Furthermore, we provide a method
for designing stabilizing gains that minimize an upper bound on the worst-case
steady-state observer error. We demonstrate our algorithm on an IEEE 14-bus
power system.
