  Self-triggered control (STC) and periodic event-triggered control (PETC) are
aperiodic sampling techniques aiming at reducing control data communication
when compared to periodic sampling. In both techniques, the effects of
measurement noise in continuous-time systems with output feedback are
unaddressed. In this work we prove that additive noise does not hinder
stability of output-feedback PETC of linear time-invariant (LTI) systems. Then
we build an STC strategy that estimates PETC's worst-case triggering times. To
accomplish this, we use set-based methods, more specifically ellipsoidal sets,
which describe uncertainties on state, disturbances and noise. Ellipsoidal
reachability is then used to predict worst-case triggering condition
violations, ultimately determining the next communication time. The ellipsoidal
state estimate is recursively updated using guaranteed state estimation (GSE)
methods. The proposed STC is designed to be computationally tractable at the
expense of some added conservatism. It is expected to be a practical STC
implementation for a broad range of applications.
