Fundamental Stealthiness–Distortion Trade-Offs in Cyber-Physical Systems

Song Fang, Quanyan Zhu

Research output: Chapter in Book/Report/Conference proceedingChapter


In this chapter, we analyze the fundamental stealthiness–distortion trade-offs of linear Gaussian open-loop dynamical systems and (closed-loop) feedback control systems under data injection attacks using a power spectral analysis, whereas the Kullback–Leibler (KL) divergence is employed as the stealthiness measure. Particularly, we obtain explicit formulas in terms of power spectra that characterize analytically the stealthiness–distortion trade-offs as well as the properties of the worst-case attacks. Furthermore, it is seen in general that the attacker only needs to know the input–output behaviors of the systems in order to carry out the worst-case attacks.

Original languageEnglish (US)
Title of host publicationSecurity and Resilience in Cyber-Physical Systems
Subtitle of host publicationDetection, Estimation and Control
PublisherSpringer International Publishing
Number of pages24
ISBN (Electronic)9783030971663
ISBN (Print)9783030971656
StatePublished - Jan 1 2022

ASJC Scopus subject areas

  • General Engineering
  • General Computer Science


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