Asynchronous consensus of agents with double-integrator dynamics

This paper is concerned with the asynchronous consensus problem of agents with double-integrator dynamics under time-invariant interaction topology. It is assumed that each agent measures its states relative to its neighbors only at discrete times and the discrete times of each agent are independent of the others´. It is shown that the asynchronous consensus is equivalent to the globally asymptotically stability of a time-varying discrete-time system with delays. Moreover, a sufficient condition for asynchronous consensus is established in virtue of the linear matrix inequality technique and the Lyapunov direct approach. Simulations are provided to illustrate the effectiveness of the theoretical results.