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Persistence based analysis of consensus protocols for dynamic graph networks
This article deals with the consensus problem involving agents with
time-varying singularities in the dynamics or communication in undirected graph
networks. Existing results provide control laws which guarantee asymptotic
consensus. These results are based on the analysis of a system switching
between piecewise constant and time-invariant dynamics. This work introduces a
new analysis technique relying upon classical notions of persistence of
excitation to study the convergence properties of the time-varying multi-agent
dynamics. Since the individual edge weights pass through singularities and vary
with time, the closed-loop dynamics consists of a non-autonomous linear system.
Instead of simplifying to a piecewise continuous switched system as in
literature, smooth variations in edge weights are allowed, albeit assuming an
underlying persistence condition which characterizes sufficient inter-agent
communication to reach consensus. The consensus task is converted to
edge-agreement in order to study a stabilization problem to which classical
persistence based results apply. The new technique allows precise computation
of the rate of convergence to the consensus value.Comment: This article contains 7 pages and includes 4 figures. it is accepted
in 13th European Control Conferenc
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