Set stability of phase-coupled agents in discrete time

The work in this paper addresses the stability of a discretized version of the well-known phase-coupled oscillator model from the physics community. The main contribution is a pair of stability proofs for a system of N phase-coupled agents. The first proof establishes asymptotic stability to the balanced set for a range KDeltaT, where K is a coupling gain and DeltaT is the time discretization. In the second proof, a reference vector in the unit ball is introduced and asymptotic stability of the phase centroid to the reference vector is guaranteed, again for a range of KDeltaT. These results are of particular interest to researchers looking to apply phase coupling to systems in which continuous communication is not possible. Possible applications of this work include cooperative target tracking and modeling of neurological processes and of biological aggregations.