  This paper considers the defense strategy of strategic topology switching for
the second-order multi-agent system under zero-dynamics attack (ZDA) whose
attack-starting time is allowed to be not the initial time. We first study the
detectability of ZDA, which is a sufficient and necessary condition of
switching topologies in detecting the attack. Based on the detectability, a
Luenberger observer under switching topology is proposed to detect the stealthy
attack. The primary advantages of the attack-detection algorithm are twofold:
(i) in detecting ZDA, the algorithm allows the defender (system operator) to
have no knowledge of the attack-starting time and the misbehaving agents (i.e.,
agents under attack); (ii) in tracking system in the absence of attacks,
Luenberger observer has no constraint on the magnitudes of observer gains and
the number of observed outputs, i.e., only one agent's observed output is
sufficient. Simulations are provided to verify the effectiveness of the
strategic topology-switching algorithm.
