The problem of consensus on a discrete multi-agent system with delay and time-variant coefficients is considered. Firstly, by constructing an appropriate control protocol and letting the position of the first agent be the reference state, the consensus problem of the original system is transformed into the asymptotic stability problem of the error system. Then, the asymptotic stability of the zero solution in the error system is investigated by using matrix norm theory, and some sufficient
conditions for the multi-agent system to achieve consensus are obtained. Finally, numerical simulations are also given to validate the correctness and effectiveness of the proposed criteria.