  Non-parametric representations of dynamical systems based on the image of a
Hankel matrix of data are extensively used for data-driven control. However, if
samples of data are missing, obtaining such representations becomes a difficult
task. By exploiting the kernel structure of Hankel matrices of irregularly
measured data generated by a linear time-invariant system, we provide
computational methods for which any complete finite-length behavior of the
system can be obtained. For the special case of periodically missing outputs,
we provide conditions on the input such that the former result is guaranteed.
In the presence of noise in the data, our method returns an approximate
finite-length behavior of the system. We illustrate our result with several
examples, including its use for approximate data completion in real-world
applications and compare it to alternative methods.
