A note on observability of nonlinear discrete-time systems

A concept of backward observability is introduced for nonlinear discrete-time control systems. According to the new definition the state variables can be expressed as functions of inputs, outputs and their backward shifts. It is shown that the new observability definition is more general for non-reversible systems than the one used typically in the literature. In case of reversible systems it is proved that backward observability is equivalent to the standard definition of observability. The new definition allows to enlarge the class of systems for which state variables can be estimated and the observers constructed.