An $H_2$-norm approach to performance analysis of networked control systems under multiplicative routing transformations

TL;DR

This work addresses the vulnerability of networked control systems to multiplicative routing attacks that modify measurement pathways without injecting energy. It develops an $H_2$-norm framework that expresses the attack impact as a ratio of steady-state energies between the performance output and the residual signal, and provides LMIs to compute this ratio for fixed routing matrices. The authors derive analytical worst-case bounds on degradation, reveal structural conditions under which stealthy routing manipulations can be most effective, and illustrate the results with a numerical example showing sizable performance loss with relatively modest routing perturbations. The study offers both practical tools for assessing attack impact and theoretical insights into the design of more robust, detectable NCSs against routing-based threats. Future work includes extending the framework to additive or time-varying attacks and exploring mitigation strategies employing controller/observer design and intentional excitation to preserve detectability.

Abstract

This paper investigates the performance of networked control systems subject to multiplicative routing transformations that alter measurement pathways without directly injecting signals. Such transformations, arising from faults or adversarial actions, modify the feedback structure and can degrade performance while remaining stealthy. An $H_2$-norm framework is proposed to quantify the impact of these transformations by evaluating the ratio between the steady-state energies of performance and residual outputs. Equivalent linear matrix inequality (LMI) formulations are derived for computational assessment, and analytical upper bounds are established to estimate the worst-case degradation. The results provide structural insight into how routing manipulations influence closed-loop behavior and reveal conditions for stealthy multiplicative attacks.

Figures (3)

• Figure 1: Multiplicative attack
• Figure 2: The effect of multiplicative attacks with diagonal $R= R_{11}00R_{11}\in S^{n_y}$. Left figure: the ratio $\frac{\Vert G_{\rm p}\Vert^2_{H_2}}{\Vert G_{\rm r}\Vert^2_{H_2}}$ is shown as a function of $R_{11}$ and $R_{22}$. The colored area represents the values of $(R_{11}, R_{22})$ for which the matrix $A_R$ is stable. The point $(1,1)$ corresponds to the attack-free case. The maximum impact occurs at $(0.685, 0.56)$, where the ratio reaches 5.35. Right figures: the corresponding values of $\Vert G_{\rm p}\Vert^2_{H_2}$ and $\Vert G_{\rm r}\Vert^2_{H_2}$ are shown separately.
• Figure 3: The effect of multiplicative attacks for different $R$. The black lines ($R=I$) represent the attack-free scenario. The red lines illustrate the worst case over all $R\in S^{n_y}$, where the ratio $\frac{\Vert G_{\rm p}\Vert^2_{H_2}}{\Vert G_{\rm r}\Vert^2_{H_2}}=\lim\limits_{t\to\infty}\frac{\mathop{\mathrm{tr}}\left\{ C_{\rm p}PC_{\rm p}^{\rm T}\right\}}{\mathop{\mathrm{tr}}\left\{ C_{{\rm r}, R}PC_{{\rm r}, R}^{\rm T}\right\}}$ reaches its maximum. The green lines correspond to a stealthy attack, where $R\in S^{n_y}$ is constrained by $\Vert G_{\rm r}\Vert^2_{H_2}<2$.

Theorems & Definitions (18)

• Remark 1
• Remark 2
• Remark 3
• Proposition 1
• proof
• Proposition 2
• proof
• Proposition 3
• proof
• Corollary 1