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A Study on Multidimensional Polynomial Matrix Realization

Author: ShenGuiPing
Tutor: LiuJinWang
School: Hunan University of Science and Technology
Course: Mathematics
Keywords: multidimensional realization Roessel Model absolutely minimal realization the base of Gr(o ¨)bner
CLC: O174.14
Type: Master's thesis
Year: 2011
Downloads: 17
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Abstract


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.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Real Analysis,Real Variable > Polynomial theory
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