On the observability of embedded polynomial dynamical systems

Testing a system for observability is of great practical relevance in technical applications. For linear systems, this problem was solved decades ago. The observability of nonlinear systems can be formally defined, but the actual verification is extremely difficult. For the subclass of poynomial systems, the observability can be decided in a finite number of calculation steps. In this paper, we provide an observability test for embedded polynomial systems. The observability test uses methods of algebraic geometry.