  This paper introduces a novel approach to concurrently design dynamic
controllers and correlated differential privacy noise in dynamic control
systems. An increase in privacy noise increases the system's privacy but
adversely affects the system's performance. Our approach optimizes the noise
distribution while shaping closed-loop system dynamics such that the privacy
noise has the least impact on system performance and the most effect on system
privacy. We further add privacy noise to both control input and system output
to privatize the system's state for an adversary with access to both
communication channels and direct output measurements. The study also suggests
tailored privacy bounds for different states, providing a comprehensive
framework for jointly optimizing system performance and privacy in the context
of differential privacy.
