ℌ∞ almost regulated synchronization and ℌ∞ almost formation for heterogeneous networks under external disturbances

We introduce the notions of “ℌ
_∞
almost regulated synchronization” and “ℌ
_∞
almost formation” for multi-agent systems subject to external disturbances and under directed interconnection structures. We assume that agents are linear, right-invertible and introspective with non-identical dynamics. The objective is to suppress the impact of disturbances on the synchronization error dynamics in terms of the ℌ
_∞
norm of the corresponding closed-loop transfer function. Inspired by the time-scale structure assignment techniques based on the singular perturbation theory, a family of observer-based protocols is introduced to achieve synchronization with any desired accuracy.