A behavioral approach to linear exact modeling

The behavioral approach to system theory provides a parameter-free framework for the study of the general problem of linear exact modeling and recursive modeling. The authors present the solution of the (continuous-time) polynomial-exponential time series modeling problem. Both recursive and nonrecursive solutions are provided and classified according to properties like complexity and controllability. It is shown, in particular, that recursive modeling corresponds to updating by means of a cascade inter-connection of systems. As a special case, the solution of several other problems, such as rational interpolation, realization, and modeling of arbitrary discrete-time time series, is obtained