  This paper presents new classes of consensus protocols with fixed-time
convergence, which enable the definition of an upper bound for consensus state
as a parameter of the consensus protocol, ensuring its independence from the
initial condition of the nodes. We demonstrate that our methodology subsumes
current classes of fixed-time consensus protocols that are based on homogeneous
in the bi-limit vector fields. Moreover, the proposed framework enables for the
development of independent consensus protocols that are not needed to be
homogeneous in the bi-limit. This proposal offers extra degrees of freedom to
implement consensus algorithms with enhanced convergence features, such as
reducing the gap between the real convergence moment and the upper bound chosen
by the user. We present two classes of fixed-time consensus protocols for
dynamic networks, consisting of nodes with first-order dynamics, and provide
sufficient conditions to set the upper bound for convergence a priori as a
consensus protocol parameter. The first protocol converges to the average value
of the initial condition of the nodes, even when switching among dynamic
networks. Unlike the first protocol, which requires, at each instant, an
evaluation of the non-linear predefined time-consensus function, hereinafter
introduced, per neighbor, the second protocol requires only a single evaluation
and ensures a predefined time-consensus for static topologies and fixed-time
convergence for dynamic networks. Predefined-time convergence is proved using
Lyapunov analysis, and simulations are carried out to illustrate the
performance of the suggested techniques. The exposed results have been applied
to the design of predefined time-convergence formation control protocols to
exemplify their main features.
