2004 Fiscal Year Final Research Report Summary
STUDY ON STRONGSTABILIZATION OF MULTIDIMENSIONAL SYSTEMS
| Project/Area Number |
15560383
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Control engineering
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| Research Institution | AKITA PREFECIURAL UNIVERSITY |
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Principal Investigator |
LI Xu AKITA PREFECTURE UNIVERSITY, FACULTY OF SYSTEMS SCIENCE AND TECHNOLOGY, ASSOCIATE PROFESSOR, システム科学技術学部, 助教授 (40252324)
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| Project Period (FY) |
2003 – 2004
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| Keywords | MULTIDIMENSIONAL SYSTEMS / STABILIZATION / STRONG STABILIZATION / SIMULTANEOUS STABILIZATION / FEEDBACK CONTROL / MATRIX FACTORIZATION / μ ANALYSIS |
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| Research Abstract |
It has been shown that the strong stabilization problem of multidimensional systems can be essentially formulated to two sub-problems: (1) construct of a stable multivariate polynomial or rational function whose manifold satisfies certain conditions, and (2) solve certain multivariate polynomial or rational function matrix equations. If the problem in (1) could be solved, then it is possible to obtain a solution to the problem of (2) by utilizing, e.g., Grobner base approach. However, as the polynomial or rational function required in (1) has to contain some specified curve or surface and simultaneously be stable, it is found extremely difficult to obtain such a polynomial or rational function by using analytical approach. Therefore, the possibility of. solution by
1. By exploiting existing results on stability test of multidimensional systems, an analytic expression for the class of stable stabilizing compensators has been proposed when the plant is restricted to be a first-order 2D/3D
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system. Further, a sufficient condition and construction procedure have been shown for the synthesis of a general stable stabilizing compensator for a general nD system.
2. In order to apply effective and efficient nD stability tests developed based on nD state-space model, it is required to realize an nD system described by transfer matrix into a state-space representation with as low order as possible, ideally the minimal one. A constructive procedure has been proposed for nD system realization which is computationally more efficient and leads to a lower order than existing realization algorithms.
3. An effective method for nD stability test and robust analysis has been proposed by utilizing the μ analysis approach. Due to the difficulties growing with the dimension, nD stability test and robust stability analysis problems remained to be challenged. In this research, it has been shown that problems of stability test and stability margin computation for an nD system described by Roesser model can be recast into a set of μ analysis problems in a unified way, and can be solved effectively by using commercially available software package.
4. It has been clarified that the pairwise simultaneous stabilizability of a plant family with certain parameter uncertainties is in fact equivalent to the stabilizability of the plant family. The obtained result is of special significance as it reveals that, the pairwise simultaneous stabilization problem can be reduced to a robust stabilization problem under certain conditions. It is well known that simultaneous stabilization problem is closely related to the strong stabilization problem.
5. Some new results for minor coprime polynomial matrix factorization have been given which relate to the conditions of nD strong stabilizability. Less
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