  The aim of this paper is to analyze a class of consensus algorithms with
finite-time or fixed-time convergence for dynamic networks formed by agents
with first-order dynamics. In particular, in the analyzed class a single
evaluation of a nonlinear function of the consensus error is performed per each
node. The classical assumption of switching among connected graphs is dropped
here, allowing to represent failures and intermittent communications between
agents. Thus, conditions to guarantee finite and fixed-time convergence, even
while switching among disconnected graphs, are provided. Moreover, the
algorithms of the considered class are shown to be computationally simpler than
previously proposed finite-time consensus algorithms for dynamic networks,
which is an important feature in scenarios with computationally limited nodes
and energy efficiency requirements such as in sensor networks. The performance
of the considered consensus algorithms is illustrated through simulations,
comparing it to existing approaches for dynamic networks with finite-time and
fixed-time convergence. It is shown that the settling time of the considered
algorithms grows slower when the number of nodes increases than with other
consensus algorithms for dynamic networks.
