  This paper introduces two sample-based formulations of incremental
input/output-to-state stability (i-IOSS), a suitable detectability notion for
general nonlinear systems. In this work we consider the case of limited output
information, i.e., measurements are only infrequently and/or irregularly
available. The output-dependent term of the sample-based i-IOSS bound is
properly modified to yield a characterization for detectability in presence of
incomplete output sequences. We provide both a non-timediscounted and a
time-discounted formulation of samplebased i-IOSS. Furthermore, conditions for
an i-IOSS system to be also sample-based i-IOSS are given and the relation
between the two formulations of sample-based i-IOSS is shown.
