Abstract
This paper provides a theoretical analysis to solve delay-induced consensus of a multi-agent system. Due to the individual differences of agents, the uncertain congestion of communication channels, and the physical characteristics of medium, time delay is ubiquitous at the moment of information transmission. We first present a generalisation of consensus algorithms, dealing with multiple agents and transmission delay and then obtain a sufficient condition for the system to experience consensus by constructing a Lyapunov function. It is proved that the system can reach consensus when the network of dynamic agents is strongly connected and detail-balanced. Numerical simulations show that increasing time delay may slow down the convergence rate of the system.
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