# Physical Watermarking for Replay Attack Detection in Continuous-time Systems

arXiv: https://arxiv.org/abs/2103.00790 · HTML: https://mlsanity.com/paper/2103.00790/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2021.

## Built on by (most cited first, 1 of 1)

- [Game-Theoretic Reinforcement Learning based Topology-Agnostic Defense for Virtual Power Plants](https://mlsanity.com/paper/2610.15183/) (2026)

## Abstract (arXiv)

Physical watermarking is a well established technique for replay attack detection in cyber-physical systems (CPSs). Most of the watermarking methods proposed in the literature are designed for discrete-time systems. In general, real physical systems evolve in continuous time. In this paper, we analyze the effect of watermarking on sampled-data continuous-time systems controlled via a Zero-Order Hold. We investigate the effect of sampling on detection performance and we provide a procedure to find a suitable sampling period that ensures detectability and acceptable control performance. Simulations on a quadrotor system are used to illustrate the effectiveness of the theoretical results.