On Discrete-Time Polynomial Systems.

摘要

Algebraic geometry is the natural tool for the study of a broad class of discrete-time nonlinear systems. This class consists of those systems described by polynomial transitions and polynomial constraints in the state set. The examples of nonlinear systems whose structure theory is today at all understood (bilinear input/output, bilinear in the state) are instances of this broad class of systems. In the present paper we show that a number of finiteness results can be derived for systems via the application of standard methods in algebraic geometry. In particular, we obtain practical tests for equality of behaviors, reachability and observability. Finally, we prove a preliminary result which gives conditions under which two systems with same input/output behavior are isomorphic. (Author)