In this technical note, we are concerned with linear matrix inequality (LMI) approaches for solving sampled-data state-feedback control design problems of linear time-invariant systems. This short contribution discusses a simple alternative to a family of LMI approaches based on the polytopic linear difference inclusion representation of the original problem. With the aid of the so-called matrix-dilation technique, the proposed condition is capable of being directly derived from the discrete-time Lyapunov inequality without the polytopic modeling. Finally, numerical experiments are given to illustrate the results.