Flocking of a locally interacting multi-agent system with a unit speed constraint

In this paper, we study the flocking behavior of a locally interacting multi-agent system with a unit speed constraint. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimation on perturbations of a linearized system, we obtain a sufficient condition imposed only on initial data and model parameters to guarantee flocking and further show that the system achieves a consensus at an exponential rate.