A Study On Multidimensional Polynomial Matrix Realization

The prevailing framework for robustness analysis and synthesis of uncertain systems requires modeling the underlying polynomial or national parametric uncertainty in the so-called linear fractional representation. It has been observed that the LFR uncertainty modeling problem is algebraically equivalent to the realization problem for multi-input, multi-output multidimensional systems by Roesser state-space model. Therefore, an effective and efficient n-D realization procedure will not only contribute significantly to n-D system theory but also to robust control theory.This thesis tends to analyze the multidimensional realization problem from two aspects respectively:On the one hand, it focuses on the aspect of constructing multidimensional Roesser state-space model or Linear Fractional representation uncertainty modeling. This algorithm is mainly based on LiXu's new research for the elementary operation approach. Through this, we can achieve a new algorithm which is more helpful when carried out in complicated realization.On the other hand, by applying the base of Gr(o|¨)bner theory, this thesis studies the absolutely minimal realization. Given any multidimensional function, we can figure out whether it has an absolutely minimal realization in theory. Correspondingly, a sufficient and necessary condition of the absolutely minimal realization is provided. Therefore, we can get an arithmetic procedure of deterministic process. Moreover, a relatively valuable conclusion and several representative examples are given out.