This paper devotes to the stability of aperiodic sampled-data systems with time-delay control, where the delays can impose a positive effect on the stability of the systems. The systems are modeled as impulsive switched systems with fixed switching laws. A novel separation theorem is presented to determine the Schur property of a matrix product and then used to obtain a less conservative stability criterion for the impulsive switched systems with fixed switching laws. By the separation theorem and a loop-functional approach, some new stability and stabilization criteria for aperiodic sampled-data systems with time-delay control are provided in terms of linear matrix inequalities. Finally, the stability and stabilization results are tested on some classical numerical examples to illustrate the efficiency of the proposed method.