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.

翻译：水印是一种用于检测高度复杂攻击的有前途的主动诊断技术，但容易受到恶意攻击者的攻击，这些攻击者利用窃听数据识别并随后移除或复制水印。本文提出了一种混合乘性水印(HMWM)方案，其中水印参数按照特定设计的分段仿射(PWA)混合系统的不可观测状态动态进行周期性更新。我们从理论层面分析了该方案对闭环性能的影响，并证明其稳定性得以保持。此外，我们从计算复杂度和系统理论两个角度证明，该方案使得窃听者难以重构水印参数。