Consensus Error Performance of Linear Multi-Agent Systems

In this paper, we investigate the consensus problem of linear time-invariant systems with respect to stochastic noises and deterministic disturbances. We consider first-order dynamic agents interconnected by a directed communication graph with time delay, and we seek to determine the best achievable performance that measures the error in achieving consensus under the influence of noises and disturbances. Our results consist of analytical expressions of the minimal error achievable, measured under both ℋ
2
and ℋ
∞
criteria. The expressions show explicitly how agent and network dynamics may interact to cast fundamentally dispersion effects on the consensus among the agents.