Observability and left invertibility of nonlinear discrete time systems with under-sampling

This paper deals with observability and left-invertibility of under-sampled systems. The concept of under-sampling of a discrete time system is introduced in the context of system theory for the first time in this article. Under-sampled systems are explained under a standard realization that allows to apply system theory. In particular, observability and left invertibility of these systems is investigated. It is shown that rewriting the under-sampled system under a standard form allows to characterize completely the observability and the left invertibility of the original system. One of the potential applications concerns the decrease of the number of output measurements without loss of observability of the original system