Multi-agent speed consensus via delayed position feedback with application to Kuramoto oscillators

We present conditions for a nonlinear single integrator multi-agent system to achieve a consensus on the derivatives of the agents' states, e.g. their speed, by comparing the state information, e.g. their position. This consensus property is even more surprising because the states themselves do not necessarily reach a consensus. We prove that consensus is reached even if the communication network between the agents introduces communication delays. As a special case, the considered model includes delay coupled Kuramoto oscillators with nonidentical natural frequencies. We apply our result to these oscillators and show that frequency entrainment is guaranteed for appropriate initial conditions.