  Cyber-physical systems (CPS) often rely on external communication for
supervisory control or sensing. Unfortunately, these communications render the
system vulnerable to cyber-attacks. Attacks that alter messages, such as replay
attacks that record measurement signals and then play them back to the system,
can cause devastating effects. Dynamic Watermarking methods, which inject a
private excitation into control inputs to secure resulting measurement signals,
have begun addressing the challenges of detecting these attacks, but have been
restricted to linear time invariant (LTI) systems. Though LTI models are
sufficient for some applications, other CPS, such as autonomous vehicles,
require more complex models. This paper develops a linear time-varying (LTV)
extension to previous Dynamic Watermarking methods by designing a matrix
normalization factor to accommodate the temporal changes in the system.
Implementable tests are provided with considerations for real-world systems.
The proposed method is then shown to be able to detect generalized replay
attacks both in theory and in simulation using a LTV vehicle model.
