Design of multiplicative watermarking against covert attacks

This paper addresses the design of an active cyberattack detection architecture based on multiplicative watermarking, allowing for detection of covert attacks. We propose an optimal design problem, relying on the so-called output-to-output ℓ
2
-gain, which characterizes the maximum gain between the residual output of a detection scheme and some performance output. Although optimal, this control problem is non-convex. Hence, we propose an algorithm to design the watermarking filters by solving the problem suboptimally via LMIs. We show that, against covert attacks, the output-to-output ℓ
2
-gain is unbounded without watermarking, and we provide a sufficient condition for boundedness in the presence of watermarks.