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