In this article, two kinds of leader-following formation control problems for second-order nonlinear multi-agent systems are investigated, that is, the cases with fixed topology and with switching topology. For the former, by constructing an appropriate Lyapunov functional and utilising linear matrix inequality (LMI) method, we propose a formation control algorithm which makes the nonlinear multi-agent systems converge to a desired formation. In addition, a formation control algorithm is also developed for coupled double-integrators with a constant reference velocity. Then we extend these results to the case when the interaction topology is switching. Numerical simulations are presented finally to demonstrate the effectiveness of the proposed results.