Abstract
This letter presents finite- and fixed-time protocols, which solve the consensus problem in multi-agent systems with time-varying directed topologies. We show that the proposed distributed protocols solve the consensus problem under switching topologies, which are jointly strongly connected. These distributed protocols homogenize the multi-agent networks, which make the overall system robust against disturbances. We employ the homogeneity property of the vector fields, graph theory, Lyapunov stability theory and convex analysis to show the finite- and fixed-time stability of the multi-agent systems. Numerical examples are presented to demonstrate the effectiveness of the proposed control methods.
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