  The data transmitted by cyber-physical systems can be intercepted and
exploited by malicious individuals to infer privacy-sensitive information
regarding the physical system. This motivates us to study the problem of
preserving privacy in data releasing of linear dynamical system using
stochastic perturbation. In this study, the privacy sensitive quantity is the
initial state value of the system. For protecting its privacy, we directly
design the covariance matrix of a Gaussian output noise to achieve a prescribed
uncertainty set in the form of hyper-ellipsoids. This is done by correlated
noise and through a convex optimization problem by considering the utility of
released signals. Compared to other available methods, our proposed technique
for designing the Gaussian output noise provides enhanced flexibility for
system designers. As a case study, the results are applied to a heating
ventilation and air conditioning system.
