This paper studies H_∞ and H₂ almost state or output synchronization of homogeneous multi-agent systems (MAS) with partial-state coupling via static protocols in the presence of external disturbances. We provide solvability conditions for designing static protocols. We characterize three classes of agents for which we can design linear static protocols for state or output synchronization of a MAS such that the impact of disturbances on the network disagreement dynamics, expressed in terms of the H_∞ and H₂ norms of the corresponding closed-loop transfer function, is reduced to arbitrarily small value. Meanwhile, the static protocol only needs rough information on the network graph, that is a lower bound for the real part and an upper bound for the modulus of the non-zero eigenvalues of the Laplacian matrix associated with the network graph. Our study focuses on three classes of agents which are squared-down passive, squared-down passifiable via output feedback and squared-down minimum-phase with relative degree 1.

本文研究ħ _∞和ħ ₂几乎状态或均相多代理系统（MAS）通过在外部干扰的情况下的静态协议部分状态耦合的输出同步。我们为设计静态协议提供了可解性条件。我们表征的一个我们可以设计为线性的状态或输出同步静态协议剂三类一个MAS使得扰动对网络分歧动力学的影响，在来表示ħ _∞和ħ ₂相应的闭环传递函数的范数减小到任意小的值。同时，静态协议只需要网络图上的粗略信息，即与网络图关联的拉普拉斯矩阵的非零特征值的实部的下限和实数的下限。我们的研究集中在三类代理上，它们是平方下降的无源，平方下降的可通过输出反馈进行钝化以及平方下降的最小相位（相对度为1）。