This paper primarily discusses the leader-following consensus problem in nonlinear second-order multi-agent systems with nonidentical nodes. Sampled-data-based protocols are applied to reach consensus. Both delay-free and input-delay protocols are proposed. Based on the Lyapunov functional approach and linear matrix inequality (LMI) method, sufficient criteria are obtained to guarantee quasi-consensus for nonlinear heterogeneous multi-agent systems. All the heterogeneous followers can track the leader within a bounded range. Furthermore, the error systems between the leader and each follower eventually converge to a convergence domain that depends on the heterogeneity among the dynamics of the agents. Additionally, leader-following consensus can also be reached as the heterogeneity vanishes. Finally, numerical simulations are provided to illustrate the theoretical results.

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