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This paper studies scale-free protocol design for ∞ almost output and regulated output synchronization of heterogeneous multi-agent systems with linear, right-invertible and introspective agents in presence of external disturbances. The collaborative linear dynamic protocol designs are based on localized information exchange over the same communication network, which do not require any knowledge of the directed network topology and spectrum of the associated Laplacian matrix. Moreover, the proposed scale-free protocols achieve ∞ almost synchronization with a given arbitrary degree of accuracy for any size of the network.

This paper studies regulated state synchronization of discrete-time homogeneous networks of non-introspective agents in presence of unknown non-uniform input delays. A scale free protocol is designed based on additional information exchange, which does not need any knowledge of the directed network topology and the spectrum of the associated Laplacian matrix. The proposed protocol is scalable and achieves state synchronization for any arbitrary number of agents. Meanwhile, an upper bound for the input delay tolerance is obtained, which explicitly depends on the agent dynamics.

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This paper studies regulated state synchronization for homogeneous discrete-time multi-agent systems (MAS) in the presence of unknown nonuniform communication delays. We consider partial state coupling, i.e., agents are coupled through part of their states. A low gain-based protocol is designed which only requires rough knowledge of the communication network, such that the state synchronization for MAS is achieved where the required synchronized trajectory is only given to some of the agents. INDEX TERMS Regulated state synchronization, discrete-time multi-agent systems, communication delays.