  Watermarking is a promising active diagnosis technique for detection of
highly sophisticated attacks, but is vulnerable to malicious agents that use
eavesdropped data to identify and then remove or replicate the watermark. In
this work, we propose a hybrid multiplicative watermarking (HMWM) scheme, where
the watermark parameters are periodically updated, following the dynamics of
the unobservable states of specifically designed piecewise affine (PWA) hybrid
systems. We provide a theoretical analysis of the effects of this scheme on the
closed-loop performance, and prove that stability properties are preserved.
Additionally, we show that the proposed approach makes it difficult for an
eavesdropper to reconstruct the watermarking parameters, both in terms of the
associated computational complexity and from a systems theoretic perspective.
