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In this paper, the fast consensus problem of high-order multi-agent systemsunder undirected topologies is considered. The direct link between theconsensus convergence rate and the control gains is established. An acceleratedconsensus algorithm based on gradient descent is proposed to optimize theconvergence rate. By applying the Routh-Hurwitz stability criterion, the lowerbound on the convergence rate is derived, and explicit control gains arederived as the necessary condition to achieve the optimal convergence rate.Moreover, a protocol with time-varying control gains is designed to achieve thefinite-time consensus. Explicit formulas for the time-varying control gains andthe final consensus state are given. Numerical examples and simulation resultsare presented to illustrate the obtained theoretical results.

Fast consensus of high-order multi-agent systems