Observability and Forward-Backward Observability of Discrete-Time Nonlinear Systems

In this paper, we study the observability properties of nonlinear discrete time systems. Two types of contributions are given. First, we present observability criteria in terms of appropriate codistributions. For particular, but significant, classes of systems we provide criteria that require only a finite number of computations. Then, we consider invertible systems (which includes discrete-time models obtained by sampling of continuous-time systems) and prove that the weaker notion of forward-backward observability is equivalent to the stronger notion of (forward) observability.