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Solution to the Common Lyapunov-Function Problem via Fusion of Numerical and thalytical Aspec

Research Project

Project/Area Number 07650489
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 計測・制御工学
Research InstitutionKyoto Institute of Technology

Principal Investigator

MORI Takehiro  Kyoto Institute of Technology, Dept.of Electronics & Information Science, Professor, 工芸学部, 教授 (60026359)

Co-Investigator(Kenkyū-buntansha) KUROE Yasuaki  Kyoto Institute of Technology, Dept.of Electronics & Information Science, Associ, 工芸学部, 助教授 (10153397)
Project Period (FY) 1995 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1996: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1995: ¥1,700,000 (Direct Cost: ¥1,700,000)
Keywordscommon Lyapunov function / quadratic Lyapunov fuction / continuous-time systems / discrete-time systems / LMI / リヤプノフ関数 / ロバスト安定性 / 線形行列不等式 / 数値解法 / 解析解法 / 二次形式
Research Abstract

1. We first tested several methods available to solve LMI,into which the common Lyapunov function problem can be recast, and found the so-called interior-point method most suitable for the present purpose. Based on this method, we developed a computation code by ourselves and used it throughout the study.
2. With knowledge or experience attained in the above computation process, we are successful in finding some subclasses of systems, continuous-time or discrete-time, that have a quadratic Lyapunov function in common. Some subclasses for low-order systems have also been found. In general, we noticed, there exists a parallel between continuous-time case and discrete-time one. This would give a further insight into the problem.
3. Since there exists a close connection between the problem in question and the quadratic stability problem of systems, we looked into the quadratic stability property of interval polynomials and obtained some results.

Report

(3 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • Research Products

    (8 results)

All Other

All Publications (8 results)

  • [Publications] 森禎弘: "不確かな離散時間線形システムの二次安定性と安定化" 電気学会論文誌・C. 115-C. 1291-1296 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Y. Mori: "A Partial Solution to the Common Lyapunov Function Problem : Continuous-Time Case" Proc. of ICARCV'96. 1064-1068 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Y.Mori et al.: "Quadratic stability and stabilization of uncertain discrete-time linear systems" Trans.IEEJ. Vol.115-C. 1291-1296 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] Y.Mori et al.: "A Partial Solution to the common Lyapunov function problem ; continuous-time case" Proc.of ICARCV '96. 1064-1068 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] 森 禎弘: "不確かな離散時間線形システムの二次安定性と安定化" 電気学会論文誌C. 115-C. 1291-1296 (1995)

    • Related Report
      1996 Annual Research Report
  • [Publications] Y.Mori: "A Partial Solution to the Common Cyopunov Function Problem:Continuous-Time Case" Proc.of ICARCV ′96. 1064-1068 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] Yoshihiro Mori: "Coosses of Discrcte Linear Systems Having Common Quadratic" Proc of 1995 American Control Confeuce. 3364-3365 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] 森 禎弘: "不確かな離散時間線形システムの二次安定性と安定化" 電気学会論文誌C. 115-C. 1291-1296 (1995)

    • Related Report
      1995 Annual Research Report

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Published: 1995-04-01   Modified: 2016-04-21  

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