Reaching a stochastic consensus in the noisy networks of linear MIMO agents： Dynamic output-feedback and convergence rate

This paper addresses the leader-following consensus problem of linear multi-agent systems（MASs） with communication noise. Each agent＇s dynamical behavior is described by a linear multi-input and multi-output（MIMO） system, and the agent＇s full state is assumed to be unavailable. To deal with this challenge, a state observer is constructed to estimate the agent＇s full state. A dynamic output-feedback based protocol that is based on the estimated state is proposed. To mitigate the effect of communication noise, noise-attenuation gains are also introduced into the proposed protocol. In this study, each agent is allowed to have its own noise-attenuation gain. It is shown that the proposed protocol can solve the mean square leader-following consensus problem of a linear MIMO MAS. Moreover, if all noise-attenuation gains are of Q（t-β）, where b∈（0,1）, the convergence rate of the MAS can be quantitatively analyzed. It turns out that all followers＇ states converge to the leader＇s state in the mean square sense at a rate of O（t-β）.