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Consensus in continuous-time multi-agent systems under discontinuous nonlinear protocols

In this paper, we provide a theoretical analysis for nonlinear discontinuous consensus protocols in networks of multiagents over weighted directed graphs. By integrating the analytic tools from nonsmooth stability analysis and graph theory, we investigate networks with both fixed topology and randomly switching topology. For networks with a fixed topology, we provide a sufficient and necessary condition for asymptotic consensus, and the consensus value can be explicitly calculated. As to networks with switching topologies, we provide a sufficient condition for the network to realize consensus almost surely. Particularly, we consider the case that the switching sequence is independent and identically distributed. As applications of the theoretical results, we introduce a generalized blinking model and show that consensus can be realized almost surely under the proposed protocols. Numerical simulations are also provided to illustrate the theoretical results.