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Algebraic Approach to Low-order LFR Uncertainty Modeling and Multidimensional Realization

Research Project

Project/Area Number 19560448
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Control engineering
Research InstitutionAkita Prefectural University

Principal Investigator

XU Li  Akita Prefectural University, システム科学技術学部, 教授 (40252324)

Project Period (FY) 2007 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords多次元システム / 線形分数表現(LFR) / 線形分数変換(LFT) / 状態空間実現 / ロバスと制御 / 変動システム / Roesser モデル / モデリング / ロバスト制御 / Roesserモデル
Research Abstract

本研究は, LFR(線形分数表現)によるシステムの不確かさモデリング問題と多次元システムの状態空間実現問題について研究し, 従来の1次元の場合との違いを解明した上, すべでの独立変数やパラメータを同時に取り扱う直接実現法と, まず一部分の変数を符号係数とみなして実現を求め, そしてこの作業を繰り返すことで全体の実現を得る繰り返し実現法との2種類の新しい代数的な実現法, およびそのアルゴリズムを提案した.

Report

(3 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • Research Products

    (31 results)

All 2009 2008 2007 Other

All Journal Article (16 results) (of which Peer Reviewed: 16 results) Presentation (11 results) Book (2 results) Remarks (2 results)

  • [Journal Article] A Constructive Approach to Minimal Realization Problem of 2D Systems2009

    • Author(s)
      H. Fan, H. Cheng, Li Xu
    • Journal Title

      Journal of Control Theory and Applications Vol.7(印刷中)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Direct-Construction Approach to Multidimensional Realization and LFR Uncertainty Modeling2008

    • Author(s)
      Li Xu, H. Fan, Z. Lin and N.K. Bose
    • Journal Title

      Multidimensional Systems and Signal Processing Vol.19, No.3-4

      Pages: 323-359

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Parameter Optimization Approach to Robust PI-Controller Design for Systems with Interval Plants2008

    • Author(s)
      Q. Wu, B. Lu, Li Xu
    • Journal Title

      Journal of Control Theory and Applications Vol.6, No.4

      Pages: 435-441

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] (Invited Paper) A Tutorial on Grobner Bases with Applications in Signals and Systems, IEEE Trans2008

    • Author(s)
      Z. Lin, Li Xu, N. K. Bose
    • Journal Title

      Circuits and Systems I : Regular Paper Vol.55, No.1

      Pages: 445-461

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Direct-Construction Approach to Multidimensional Realization and LFR Uncertainty Modeling2008

    • Author(s)
      Li Xu, H. Fan, Z. Lin, N. K. Bose
    • Journal Title

      Multidimensional Systems and Signal Processing Vol. 19, No. 3-4

      Pages: 323-359

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Parameter Optimization Approach to Robust PI-Controller Design for Systems with Interval Plants2008

    • Author(s)
      Q. Wu, B. Lu, Li Xu
    • Journal Title

      Journal of Control Theory and Applications Vol. 6, No. 4

      Pages: 435-441

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Constructive Approach to Minimal Realization Problem of 2D Systems2008

    • Author(s)
      H. Fan, H. Cheng, Li Xu
    • Journal Title

      Journal of Control Theory and Applications Vol. 7, No. 2(印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] (Invited Paper) A Tutorial on Grobner Bases with Applications in Signals and Systems2008

    • Author(s)
      Z. Lin, Li Xu, N. K. Bose
    • Journal Title

      IEEE Trans. Circuits and Systems I: Regular Paper 55

      Pages: 445-461

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Parameter Optimization Approach to Robust PI-Controller Design for Systems with Interval Plants2008

    • Author(s)
      Q. Wu, B. Lu, Li Xu
    • Journal Title

      Journal of Control Theory and Applications (掲載確定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Constructive Approach to Minimal Realization Problem of 2D Systems2008

    • Author(s)
      H. Fan, H. Cheng, Li Xu
    • Journal Title

      Journal of Control Theory and Applications (掲載確定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Direct-Construction Approach to Multidimensional Realization and LFR Uncertainty Modeling2008

    • Author(s)
      Li Xu, H. Fan, Z. Lin and N.K. Bose
    • Journal Title

      Multidimensional Systems and Signal Processing (掲載確定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Two-Stage Approach to the Establishment of State-Space Formulation of 2D Frequency Transformation, IEEE Trans2007

    • Author(s)
      S. Yan, Li Xu, Y. Anazawa
    • Journal Title

      Signal Processing Letters Vol.14, No.12

      Pages: 960-963

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A New Constructive Procedure for 2D Coprime Realization of Fornasini-Marchesini Model, IEEE Trans2007

    • Author(s)
      Li Xu, Q. Wu, Z. Lin and Y. Xiao
    • Journal Title

      Circuits and Systems I : Regular Papers Vol.54, No.9

      Pages: 2061-2069

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A New Constructive Procedure for 2D Coprime Realization of Fornasini-Marchesini Model2007

    • Author(s)
      Li Xu, Q. Wu, Z. Lin and Y. Xiao
    • Journal Title

      IEEE Trans. Circuits and Systems I: Regular Papers 54

      Pages: 2061-2069

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Two-Stage Approach to the Establishment of State-Space Formulation of 2D Frequency Transformation2007

    • Author(s)
      S. Yan, Li Xu, Y. Anazawa
    • Journal Title

      IEEE Trans. Signal Processing Letters 14

      Pages: 960-963

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Simple State-Space Formulations of 2-D Frequency Transformation and Double Bilinear Transformation

    • Author(s)
      S. Yan, N. Shiratori, Li Xu
    • Journal Title

      Multidimensional Systems and Signal Processing (掲載予定)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Presentation] Structural Insights and Constructive Procedures for Multidimen sional Realization and LFR Uncertainty Modeling2008

    • Author(s)
      Li Xu
    • Organizer
      SICE Annual Conference 2008
    • Place of Presentation
      Tokyo, Japan
    • Year and Date
      2008-08-22
    • Related Report
      2008 Annual Research Report
  • [Presentation] Synthesis of Multidimensional Control Systems by Grobner Basis Approach2008

    • Author(s)
      Li Xu
    • Organizer
      SICE Annual Conference 2008
    • Place of Presentation
      Tokyo, Japan
    • Year and Date
      2008-08-21
    • Related Report
      2008 Annual Research Report
  • [Presentation] New Results on State-Space Formulation of 2-D Frequency Transf ormation2008

    • Author(s)
      S. Yan, N. Shiratori, Li Xu
    • Organizer
      CCDC2008
    • Place of Presentation
      Yantai, China
    • Year and Date
      2008-07-02
    • Related Report
      2008 Annual Research Report
  • [Presentation] Derivation of a Novel State-Space Formulation of 2-D Frequency Transformation by LFT Techniques2008

    • Author(s)
      N. Shiratori, S. Yan, Li Xu
    • Organizer
      ICEMS2008
    • Place of Presentation
      Wuhan, China
    • Related Report
      2008 Annual Research Report 2008 Final Research Report
  • [Presentation] Synthesis of Multidimensional Control Systems by Grobner Basis Approach2008

    • Author(s)
      Li Xu
    • Organizer
      SICE2008
    • Place of Presentation
      Tokyo, Japan
    • Related Report
      2008 Final Research Report
  • [Presentation] Structural Insights and Constructive Procedures for Multidimensional Realization and LFR Uncertainty Modeling2008

    • Author(s)
      Li Xu
    • Organizer
      SICE 2008
    • Place of Presentation
      Tokyo, Japan
    • Related Report
      2008 Final Research Report
  • [Presentation] New Results on State-Space Formulation of 2-D Frequency Transformation2008

    • Author(s)
      S. Yan, N. Shiratori, Li Xu
    • Organizer
      CCDC2008
    • Place of Presentation
      Yantai, China
    • Related Report
      2008 Final Research Report
  • [Presentation] State-Space Formulation of 2D Frequency Transformation for 2D Digital Filters2007

    • Author(s)
      S. Yan, Li Xu, Y. Anazawa
    • Organizer
      2007 International Workshop on Multidimensional (nD) Systems (NDS07)
    • Place of Presentation
      Aveiro, Portugal
    • Year and Date
      2007-06-07
    • Related Report
      2007 Annual Research Report
  • [Presentation] Revisiting the Absolutely Minimal Realization for Two-dimensional Digital Filters2007

    • Author(s)
      Z. Lin, Li Xu, Y. Anazawa
    • Organizer
      2007 IEEE International Symposium on Circuits and Systems (ISCAS2007)
    • Place of Presentation
      New Orleans, USA
    • Year and Date
      2007-05-07
    • Related Report
      2007 Annual Research Report
  • [Presentation] State-Space Formulation of 2D Frequency Transformation for 2D Digital Filters2007

    • Author(s)
      S. Yan, Li Xu, Y. Anazawa
    • Organizer
      NDS07
    • Place of Presentation
      Aveiro, Portugal
    • Related Report
      2008 Final Research Report
  • [Presentation] Revisiting the Absolutely Minimal Realization for Two-dimensional Digital Filters2007

    • Author(s)
      Z. Lin, Li Xu, Y. Anazawa
    • Organizer
      ISCAS2007
    • Place of Presentation
      New Orleans
    • Related Report
      2008 Final Research Report
  • [Book] "Applications of Grobner bases in synthesis of multidimensional control systems", in Grobner Bases in Control Theory and Signal Processing(Eds. Hyungju Park, Georg Regensburger)2007

    • Author(s)
      Li Xu
    • Publisher
      Walter de Gruyter
    • Related Report
      2008 Final Research Report
  • [Book] Grobner Bases in Control Theory and Signal Processing (Eds. Hyungju Park, Georg Regensburger)2007

    • Author(s)
      Li Xu
    • Publisher
      Walter de Gruyter
    • Related Report
      2007 Annual Research Report
  • [Remarks]

    • URL

      http://web.sc.eis.akita-pu.ac.jp/~xuli/

    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      http://web.sc.eis.akita-pu.ac.jp/~xuli/pulist.html

    • Related Report
      2008 Annual Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

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