  A model is proposed for a class of asynchronous sample-and-hold operators
that is relevant in the analysis of embedded and networked systems. The model
is parametrized by characteristics of the corresponding time-varying
input-output delay. Uncertainty in the relationship between the timing of
zero-order-hold update events at the output and the possibly aperiodic sampling
events at the input means that the delay does not always reset to a fixed
value. This is distinct from the well-studied synchronous case in which the
delay intermittently resets to zero at output update times. The main result
provides a family of integral quadratic constraints that covers the proposed
model. To demonstrate an application of this result, robust $\mathbf{L}_2$
stability and performance certificates are devised for an asynchronous
sampled-data implementation of a feedback loop around given linear
time-invariant continuous-time open-loop dynamics. Numerical examples are also
presented.
