On the Convergence Properties of a Heterogeneous Multiagent System on the Unit Sphere

We establish the convergence of a heterogeneous multiagent system on the unit sphere in even-dimensional Euclidean space. In this work, we show that all relative distances converge to some definite values, when the natural frequencies are completely determined diagonal matrices with half-dimension and the coupling strength is sufficiently larger than the maximal differences of the natural frequencies. Our result extends the previous results about practical aggregation where the maximal distance is merely bounded by the inverse of the coupling strength without convergence.