Stability of a second order consensus algorithm with time delay

In this paper, we investigate a second order consensus problem in a directed graph with non-uniform time delay. This problem arises naturally in real multi-agent systems such as distributed sensing and collective motion. We analyze convergence of the consensus algorithm by frequency domain methods. By using the small -¿ stability theorem, we derive criteria to guarantee convergence. Furthermore, we extend the analysis to higher order systems with time delay. Finally, we present simulations to illustrate theoretical results.