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This note extends the prior work in L2 stability of self-triggered feedback systems, where the next task release time and finishing time are predicted based on the sampled states. A self-triggering scheme is proposed, which relaxes the assumption in the prior work that the magnitude of the process noise is bounded by a linear function of the norm of the system state. We show that the sample periods generated by this scheme are always greater than a positive constant. We also provide state-based deadlines for delays and propose a way that may enlarge those deadlines without breaking L2 stability.