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This note analyzes the stability properties of a group of mobile agents that align their velocity vectors, and stabilize their inter-agent distances, using decentralized, nearest-neighbor interaction rules, exchanging information over networks that change arbitrarily (no dwell time between consecutive switches). These changes introduce discontinuities in the agent control laws. To accommodate for arbitrary switching in the topology of the network of agent interactions we employ nonsmooth analysis. The main result is that regardless of switching, convergence to a common velocity vector and stabilization of inter-agent distances is still guaranteed as long as the network remains connected at all times.
Tanner et al. (Tue,) studied this question.