  This paper deals with the output regulation problem (ORP) of a linear
time-invariant (LTI) system in the presence of sporadically sampled measurement
streams with the inter-sampling intervals following a stochastic process. Under
such sporadically available measurement streams, a regulator consisting of a
hybrid observer, continuous-time post-processing internal model, and stabilizer
are proposed, which resets with the arrival of new measurements. The resulting
system exhibits a deterministic behavior except for the jumps that occur at
random sampling times and therefore the overall closed-loop system can be
categorized as a piecewise deterministic Markov process (PDMP). In existing
works on ORPs with aperiodic sampling, the requirement of boundedness on
inter-sampling intervals precludes extending the solution to the random
sampling intervals with possibly unbounded support. Using the Lyapunov-like
theorem for the stability analysis of stochastic systems, we offer sufficient
conditions to ensure that the overall closed-loop system is mean exponentially
stable (MES) and the objectives of the ORP are achieved under stochastic
sampling of measurement streams. The resulting LMI conditions lead to a
numerically tractable design of the hybrid regulator. Finally, with the help of
an illustrative example, the effectiveness of the theoretical results are
verified.
