Research in Applied Mathematics Related to Mathematical System Theory.

摘要

This report deals with research results obtained in the field of mathematical system theory. Special emphasis was given to the following areas: (1) Linear system theory over a field: parametrization of multi-input, multi-output systems and the geometric structure of classes of systems of constant dimension. (2) Linear systems over a ring: development of the theory for very general classes of rings. (3) Nonlinear system theory: basic properties of polynomial (discrete-time) systems and their realization theory. The present report is only a brief summary of findings, which are far too technical to be explained in a few pages. The results are being gradually published in the open literature. For details, refer to previous proposals and/or to the publications listed in the references.