Applied Mathematics & Information Sciences

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High-order consensus, in which individual high-order dynamic units keep in pace with each other in a distributed fashion, depends both on the feedback gains of the protocol and on the properties of the interaction network. By employing a frequency domain method, we explicitly derive analytical equations that clarify a rigorous connection between the stability of general high-order consensus and the system parameters such as the network topology and feedback gains. Using the derived consensus polynomials, the general sufficient and necessary stability criterion is obtained for high-order consensus networks of arbitrary topology. Furthermore, a sufficient condition of desirable time complexity for high-order consensus is given by exploiting the topology properties of underlying networks. Numerical simulation results are provided to demonstrate the effectiveness of our theoretical results.

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