The stability of consensus in linear and nonlinear multi-agent systems with periodically switched communication topology is studied using Floquet theory. The proposed strategy is illustrated for the cases of consensus in linear single-integrator, higher-order integrator, and leader-follower consensus. In addition, the application of Floquet theory in analyzing special cases such as switched systems with joint connectivity, unstable subsystems, and nonlinear systems, including the use of feedback linearization and local linearization in the Kuramoto model, is also studied. By utilizing Floquet theory for multi-agent systems with periodically switched communication topologies, one can simultaneously evaluate the effects of each subsystem’s convergence rate and dwell time on overall behavior. Numerical simulation results are presented to demonstrate the efficacy of the proposed approach in stability analysis of all these cases.
A new strategy for full pose and velocity consensus control of multi-agent rigid body systems in the presence of communication delays is presented. Specifically, consensus protocols are proposed for a system of N heterogeneous rigid bodies on the Banach manifold associated with the tangent bundle TSE(3) N , under a fixed and undirected communication topology, where the attitudes of the rigid bodies are described in terms of rotation matrices. The stability argument is strengthened from that used in prior studies by using an extension of Morse-Lyapunov-Krasovskii approach, and sufficient conditions are derived to achieve almost global asymptotic stability of the consensus subspace. Finally, illustrative examples are given to demonstrate the proposed method where both homogenous and heterogeneous communication delays are considered.
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