In this paper, we study regulated output synchronization for continuous- or discrete-time heterogeneous multi-agent systems with linear right-invertible agents subject to unknown, nonuniform and arbitrarily large communication delays. It is assumed that all the agents are introspective, meaning that they have access to their own local measurements. A scale-free design framework utilizing localized information exchange has been adopted. The scale-free protocol design is solely based on the knowledge of the agent models such that we do not require any information about the communication networks and the number of agents.