  We consider trajectories where the sign of the derivative of each entry is
opposite to that of the corresponding entry in the gradient of an energy
function. We show that this condition guarantees convergence when the energy
function is quadratic and positive definite and partly extend that result to
some classes of positive semi-definite quadratic functions including those
defined using a graph Laplacian. We show how this condition allows establishing
the convergence of a platoon application in which it naturally appears, due to
deadzones in the control laws designed to avoid instabilities caused by
inconsistent measurements of the same distance by different agents.
