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This paper deals with the problem of stability and stabilization of sampled-data systems under asynchronous samplings and actuator saturation. The method is based, on the one hand, on the use of a novel class of Lyapunov functionals whose derivative is negative along the trajectories of the continuous-time model of the sampled data system. It is shown that this fact guarantees that a quadratic Lyapunov function is strictly decreasing for the discrete-time asynchronous system. On the other hand, the control saturation is taken into account from the use of a generalized sector condition. These ingredients lead to the formulation of improved LMI conditions that can be cast in optimization problems aiming at enlarging estimates of the region of attraction of the closed-loop system or maximizing the bounds on the sampling period jitter for which stability and stabilization are ensured.