H∞ & H2 almost state synchronization with full-state coupling for homogeneous multi-agent systems

This paper studies the H∞ and H2 almost state synchronization problem for homogeneous multi-agent systems with general linear agents affected by external disturbances and a directed communication topology. Agents are connected via diffusive full-state coupling, i.e. agents are coupled through states. A necessary and sufficient condition is developed for the solvability of the H∞ and H2 almost state synchronization problem. Moreover, a family of static protocols are developed such that the impact of disturbances on the network disagreement dynamics, expressed in terms of the H∞ and H2 norm of the corresponding closed-loop transfer function, is reduced to any arbitrarily small value. The protocol design is based on two methods: algebraic Riccati equation (ARE) or asymptotic time-scale eigenstructure assignment (ATEA).