  In this two-part paper, we consider strategic topology switching for the
second-order multi-agent systems under a special class of stealthy attacks,
namely the "zero-dynamics" attack (ZDA). The main mathematical tool proposed
here is to strategically switch the network topology to detect a possible ZDA.
However, it is not clear a priori that such a switching strategy still yields
consensus in this switched system, in the normal (un-attacked) operation mode.
In Part I, we propose a strategy on the switching times that enables the
topology-switching algorithm proposed in Part II to reach the second-order
consensus in the absence of a ZDA. Utilizing the theory of stable switched
linear systems with unstable subsystems, we characterize sufficient conditions
for the dwell time of topology-switching signal to reach consensus. Building on
this characterization, we then propose a decentralized time-dependent
topology-switching algorithm. The proposed algorithm, used in conjunction with
a simplified control protocol, achieves consensus while providing substantial
advantages over other control approaches: it relies only on the relative
position measurements (without any requirement for velocity measurements); and
it does not impose any constraint on the magnitudes of coupling weights. We
finally demonstrate our theoretical findings via the numerical simulation
results.
