Some geometric and algebraic methods applied in multidimensional systems theory: around the problem of strong stabilizability of n-D systems

摘要

In this article the stability, stabilizability and strong stabilizability of multidimensional (n-ID) linear systems are considered. The main purpose is to give a review of some algebraic, geometric, analyitic and symbolic compuatational methods applied for solving related problems. While the focus is on a method called Cylindrical Algebraic Decompostion (CAD) for analyzing real algebraic varieties and semi-algebraic sets, ideas from several variable analysis used for proving some fundamental theorems are explained. A related topic: the pole placement problem and its algebraic geometric aspect will be briefly mentioned.