Sample-Based Nonlinear Detectability for Discrete-Time Systems

This article 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 the presence of incomplete output sequences. We provide both a nontime-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.