  In this paper, we propose and analyze an attack detection scheme for securing
the physical layer of a networked control system against attacks where the
adversary replaces the true observations with stationary false data. An
independent and identically distributed watermarking signal is added to the
optimal linear quadratic Gaussian (LQG) control inputs, and a cumulative sum
(CUSUM) test is carried out using the joint distribution of the innovation
signal and the watermarking signal for quickest attack detection. We derive the
expressions of the supremum of the average detection delay (SADD) for a
multi-input and multi-output (MIMO) system under the optimal and sub-optimal
CUSUM tests. The SADD is asymptotically inversely proportional to the expected
Kullback-Leibler divergence (KLD) under certain conditions. The expressions for
the MIMO case are simplified for multi-input and single-output systems and
explored further to distil design insights. We provide insights into the design
of an optimal watermarking signal to maximize KLD for a given fixed increase in
LQG control cost when there is no attack. Furthermore, we investigate how the
attacker and the control system designer can accomplish their respective
objectives by changing the relative power of the attack signal and the
watermarking signal. Simulations and numerical studies are carried out to
validate the theoretical results.
