Consensus problems in networks of agents with double-integrator dynamics and time-varying delays

In this article, we consider consensus problems in networks of agents with double-integrator dynamics and non-uniform time-varying delays. The agent dynamics is adopted as a typical point mass model based on Newton's law. Without assuming that the weighting factors in the information update schemes are non-negative, we propose two protocols such that both the state and the velocity of agents achieve consensus. An equivalent reduced-order system is introduced to analyse the convergence of the protocols. Some necessary and (or) sufficient conditions for consensus are established in terms of linear matrix inequalities. Simulation results are provided that demonstrate the effectiveness of our theoretical results.