Exact Consensus Error for Multi-agent Systems with Additive Noises

In this paper, the consensus problem is investigated for discrete-time multi-agent systems with additive process noises. Due to the presence of additive noises in the system dynamics, consensus cannot be achieved. The main contribution of this paper is to give the exact consensus error. In particular, control gain depending on the agent dynamics and network topology is designed based on the technique dealing with the simultaneous stabilization. Finally, a numerical simulation is provided to demonstrate the effectiveness of the proposed theoretical results.