  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 l2-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 l2-gain is unbounded
without watermarking, and we provide a sufficient condition for boundedness in
the presence of watermarks.
