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We consider trajectories where the sign of the derivative of each entry isopposite to that of the corresponding entry in the gradient of an energyfunction. We show that this condition guarantees convergence when the energyfunction is quadratic and positive definite and partly extend that result tosome classes of positive semi-definite quadratic functions including thosedefined using a graph Laplacian. We show how this condition allows establishingthe convergence of a platoon application in which it naturally appears, due todeadzones in the control laws designed to avoid instabilities caused byinconsistent measurements of the same distance by different agents.

Trajectory convergence from coordinate-wise decrease of quadratic energy functions, and applications to platoons