In this paper, we consider a discrete-time consensus network, and assume that one of the agents acts as a leader and injects an input signal to improve the overall system performance, in particular to increase the speed of convergence to consensus or to achieve finite-time consensus. Two possible control protocols are proposed, and the characteristic polynomials of the resulting closed-loop systems are determined. These results allow us to investigate the consensus and finite-time consensus of the overall systems. Open problems and future research directions conclude this paper.