Global Observability of Discrete-Time Polynomial Systems

We consider the global observability of general discrete-time polynomial systems with feed-through terms. In testing the observability of discrete-time nonlinear systems, it is not guaranteed that a finite set of conditions is sufficient. Referring to results from commutative algebra, we show that only a finite set of conditions characterizes the observability of the polynomial systems. Finally, examples demonstrate the proposed criterion for testing the observability.