  Privacy breaches of cyber-physical systems could expose vulnerabilities to an
adversary. Here, privacy leaks of step inputs to linear-time-invariant systems
are mitigated through additive Gaussian noise. Fundamental lower bounds on the
privacy are derived, which are based on the variance of any estimator that
seeks to recreate the input. Fully private inputs are investigated and related
to transmission zeros. Thereafter, a method to increase the privacy of optimal
step inputs is presented and a privacy-utility trade-off bound is derived.
Finally, these results are verified on data from the KTH Live-In Lab Testbed,
showing good correspondence with theoretical results.
