This paper is concerned with the consensus of multiagent systems with nonlinear dynamics through the use of aperiodic sampled-data controllers, which are more flexible than classical periodic sampled-data controllers. By input delay approach, the resulting sampled-data system is reformulated as a continuous system with time-varying delay in the control input. A continuous Lyapunov functional, which captures the information on sampling pattern, together with the free-weighting matrix method, is then used to establish a sufficient condition for consensusability. For a more general case that the sampled-data controllers are subject to constant input delays, a novel discontinuous Lyapunov functional is introduced on the basis of the vector extension of Wirtinger's inequality. This functional can lead to simplified and efficient stability conditions for computation and optimization. Further results on the estimate of maximal allowable sampling interval upper bound is given as well. Numerical example is provided to show the effectiveness and merits of the proposed protocol.