The Designated Convergence Rate Problem of Consensus or Flocking of Double-Integrator Agents With General Non-Equal Velocity and Position Couplings

This technical note considers consensus or flocking of coupled multiple double-integrator agents, in which the velocity coupling and position coupling (VCPC) between agents, respectively, are generally non-equal, differing from the equal VCPC setting in the vast literature. This technical note addresses the problem in two aspects: the convergence condition, and particularly the designated convergence rate (or designated convergence margin) condition that was rarely investigated for either flocking, formation, or consensus. Correspondingly, this technical note has two contributions: 1) some necessary and sufficient convergence conditions for flocking or consensus are established, which extend the existing results in the field; and particularly 2) some necessary and sufficient conditions are derived, to guarantee the designated convergence rate of consensus or flocking, which are more valuable for systems design than just convergence analysis performed by most other works on multi-agent systems.