  This work is concerned with stochastic consensus conditions of multi-agent
systems with both time-delays and measurement noises. For the case of additive
noises, we develop some necessary conditions and sufficient conditions for
stochastic weak consensus by estimating the differential resolvent function for
delay equations. By the martingale convergence theorem, we obtain necessary
conditions and sufficient conditions for stochastic strong consensus. For the
case of multiplicative noises, we consider two kinds of time-delays, appeared
in the measurement term and the noise term, respectively. We first show that
stochastic weak consensus with the exponential convergence rate implies
stochastic strong consensus. Then by constructing degenerate Lyapunov
functional, we find the sufficient consensus conditions and show that
stochastic consensus can be achieved by carefully choosing the control gain
according to the noise intensities and the time-delay in the measurement term.
