Abstract
This chapter studies the consensus problem for multi-agent systems with agents characterized by high-order linear systems with time delays existing in both the communication network and inputs of the agents. Under the condition that the open-loop dynamics of the agents is at most polynomially unstable and the communication topology among the agents contains a directed spanning tree, the TPF approach is established to solve the consensus problems. It is proven that if the delays are exactly known, the consensus problems can be solved by both full-state feedback and (full-order and reduced-order) observer-based output feedback protocols for arbitrarily large yet bounded delays. On the other hand, the communication delays and input delays can be allowed to be time-varying, arbitrarily large yet bounded, and even unknown, if the open-loop dynamics of the agents only contain zero eigenvalues.
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