  This paper aims at secure and privacy preserving consensus algorithms of
networked systems. Due to the technical challenges behind decentralized design
of such algorithms, the existing results are mainly restricted to a network of
systems with simplest first-order dynamics. Like many other control problems,
breakthrough of the gap between first-order dynamics and higher-order ones
demands for more advanced technical developments. In this paper, we explore a
Paillier encryption based average consensus algorithm for a network of systems
with second-order dynamics, with randomness added to network weights. The
conditions for privacy preserving, especially depending on consensus rate, are
thoroughly studied with theoretical analysis and numerical verification.
