  Exponential dichotomies play a central role in stability theory for dynamical
systems. They allow to split the state space into two subspaces, where all
trajectories in one subspace decay whereas all trajectories in the other
subspace grow, uniformly and exponentially. This paper studies uniform
detectability and observability notions for linear time varying systems, which
admit an exponential dichotomy. The main contributions are necessary and
sufficient detectability conditions for this class of systems.
