Squared-down passivity based H∞ almost synchronization of homogeneous continuous-time multi-agent systems with partial-state coupling via static protocol

This paper studies H∞ almost state and output synchronizations of homogeneous multi-agent systems (MAS) with partial-state coupling with general linear agents affected by external disturbances. We will characterize when static linear protocols can be designed for state and output synchronization for a MAS such that the impact of disturbances on the network disagreement dynamics, expressed in terms of the H∞ norms of the corresponding closed-loop transfer function, is reduced to any 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.