This paper considers the problem of decentralized goal assignment and trajectory generation for multi-robot networks when only local communication is available, and proposes an approach based on methods related to switched systems and set invariance. A family of Lyapunov-like functions is employed to encode the (local) decision making among candidate goal assignments, under which the agents pick the assignment which results in the shortest total distance to the goals. An additional family of

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... punov-like barrier functions is activated in the case when the optimal assignment may lead to colliding trajectories, thus maintaining system safety while preserving the convergence guarantees. The proposed switching strategies give rise to feedback control policies which are scalable as the number of agents increases, and therefore are suitable for applications including first-response deployment of robotic networks under limited information sharing. Simulations demonstrate the efficacy of the proposed method.