Consensus of Linear Multivariable Discrete-Time Multiagent Systems: Differential Privacy Perspective

Differential privacy, which has been widely applied in industries, is a privacy mechanism effective in preventing malicious entities from breaching the privacy of an individual participant. It is usually achieved by adding random variables in the data. This article investigates a class of multivariable discrete-time multiagent systems with
$\epsilon $
-differential privacy preserved. A novel information-masking mechanism is proposed, in which the information of each state transmitted to different neighbors is obscured by adding independent random noises. Then, the mean-square consensus conditions, and the upper bound and lower bound of the convergence rate are obtained. Moreover, the conditions for the convergence rate reaching its upper bound are established. The results can be applied to the average mean-square consensus. In addition, a necessary and sufficient condition is presented under which agents can preserve the dynamics of agents
$\epsilon $
-differentially private at any time instant.