Sample-based nonlinear detectability for discrete-time systems

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-time-discounted and a time-discounted formulation of sample-based 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.