Consensus and convergence rate analysis for multi-agent systems with time delay

In this paper, we are concerned with the consensus problem for multi-agent systems with time delay. The consensus problem is taken as a root finding problem in stochastic approximation to deal with. Via choosing an appropriate regression function, the multi-agent system with a finite delay achieves asymptotic consensus. Furthermore, we establish a relationship between the convergence rate and the exponent of the step size of the algorithm. It is worth mentioning that the convergence rate only depends on the step size rather than the delay.