Self-Triggering Under State-Independent Disturbances

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.