  We address the problems of bearing-only consensus and formation control,
where each agent can only measure the relative bearings of its neighbors and
relative distances are not available. We provide stability results for the
Filippov solutions of two gradient-descent laws from non-smooth Lyapunov
functions in the context of differential inclusion. For the consensus and
formation control problems with undirected sensing topologies, we prove
finite-time and asymptotic convergence of the proposed non-smooth gradient
flows. For the directed consensus problem, we prove asymptotic convergence
using a different non-smooth Lyapunov function given that the sensing graph has
a globally reachable node. Finally, For the directed formation control problem
we prove asymptotic convergence for directed cycles and directed acyclic graphs
and also introduce a new notion of bearing persistence which guarantees
convergence to the desired bearings.
