A large class of multi-agent systems can be described by second-order and third-order models in practical applications. In this paper, we consider the consensus and the optimization problem of convergence rate of second-order and third-order multi-agent systems under undirected topologies. A constant control protocol is applied to discrete-time agents. First, a necessary and sufficient condition for consensus is presented, as well as the explicit formula of the consensus state. Then, we transform the problem of accelerated consensus into the optimization problem of convergence rate. Explicit formulas for the optimal convergence rate and control gains of second-order and third-order multi-agent systems are obtained by applying the Routh criterion. Finally, simulation examples are given to illustrate the effectiveness of the theoretical results.