Secure estimation for unstable systems

We assume that the states of an unstable dynamical system are encoded and sent to an estimator through an uncertain channel, which is a channel disturbing its inputs in a nonstochastic manner. The encoder's codeword is also fed into another uncertain channel, at whose output an eavesdropper is listening. The estimator should obtain a uniformly bounded system state estimation error, whereas the eavesdropper's information about the system states should be subject to a security constraint. We find a condition on the relation between the uncertain channel from encoder to estimator and the uncertain channel from encoder to eavesdropper which if satisfied allows for at least one of the two following security criteria to hold: The volume of the set of states possible acccording to the eavesdropper's information tends to infinity at exponential speed-by itself (strong security) or if divided by the volume of the set of states possible according to the estimator's information (weak security).