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Computer Generation of Lyapunov Functions and Its Applications

Research Project

Project/Area Number 05650371
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field System engineering
Research InstitutionKobe University

Principal Investigator

HANEDA Hiromasa  Kobe University, Dept.of Elec.& Electr.Eng., Professor, 工学部, 教授 (10031113)

Co-Investigator(Kenkyū-buntansha) TAGAWA Kiyoharu  Kobe University, Dept.of Elec.& Electr.Eng., Assistant Professor, 工学部, 助手 (50252789)
OHTA Yuzo  Kobe University, Dept.of Elec.& Electr.Eng., Associate Professor, 工学部, 助教授 (80111772)
Project Period (FY) 1993 – 1994
Project Status Completed (Fiscal Year 1994)
Budget Amount *help
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1994: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 1993: ¥1,600,000 (Direct Cost: ¥1,600,000)
KeywordsLyapunov Functions / Nonlinear Systems / Estimate of Stability Regions / Computer Generation of Lyapunov Functions / Genelarization of Sector Condition / Dynamic Convex Hull Algorithm / Variable Structure Control System / リヤプノフ関数の自動生成 / 安定解析 / 計算機による自動生成
Research Abstract

1. Algorithm for lmproving polytope lyapunov Function : We examined several method to improve polytope Lyapunov functions, and we conclude that the most useful method is that adding vectors which are extreme points of vector field generated by the generalized sector conditions to the present polytope. Moreover, by using real Jordan canonical form, we proposed a method to generate useful an initial polytope.
2. Dynamic Convex Hull Algorithm : We proposed a new dynamic convex hull algorithm which requires less memories and computing time than the Beneath-Beyond method.
3. Discontinuous Systems : We derived a stability result for discontinuous systems which may have sliding modes. The result is almost same with that for continuous systems. Moreover, by using a polytope Lyapunov function, we proposed a design method for variable structure control systems. This method can eliminate chattering.
4. Applications : We applied the polytope Lyapunov function to the stability analysis of composite systems. We also applied it to the stability analysis of fussy control systems, and showed that, by applying generalized sector conditions, we can guarantee the stability with less conservative conditions than the traditional Lyapunov functions such as quadratic Lyapunov functions and so on.

Report

(3 results)
  • 1994 Annual Research Report   Final Research Report Summary
  • 1993 Annual Research Report
  • Research Products

    (15 results)

All Other

All Publications (15 results)

  • [Publications] Y.Ohta: "Computer generalized Lyapunov functions for a class of nonlinear systems" IEEE Trans. on Circuits and Systems-I. 40. 343-354 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] 太田有三: "リアプノフ関数の自動生成と安定領域の推定" 電子情報通信学会論文誌A. J76-A. 1286-1293 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] 太田有三: "凸多面体Lyapunov関数と動的凸包算法" システム制御情報学会誌. 38. 147-154 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] 太田有三: "凸多面体リアプノフ関数の不連続系への応用について" システム制御情報学会論文誌. 7. 228-230 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y. Ohta: "Computer Genaration of Lyapunov Function and Estimate of a Stability Region" Electronics and Communications in Japan, Part3: Fundamental Electronic Science. 77. 44-54 (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Ohta: "Computer generalized Lyapunov functions for a class of nonlinear systems." IEEE Trans.on Circuits and Systems-I. vol.40. 343-354 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Ohta: "Computer Generation of Lyapunov Functions and Estimate of a Stability Region." The Trans.of The Inst.of Electronics, Information and Communication Engineers A. vol.J76-A. 1286-1293 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Ohta: "Polytope Lyapunov Functions and Dynamic Convex Hull Algorithms." Systems, Control and Information. vol.38. 147-154 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Ohta: "A Note on the Application of Polytope Lyapunov Function for Discontinuous Systems." The Inst.of Systems, Control and Information Engineers. vol.7. 228-230 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] Y.Ohta: "Computer Generation of Lyapunov Function and Estimate of a Stability Region." Electronics and Communications in Japan, Part3 : Fundamental Electronic Science. vol.77. 44-54 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1994 Final Research Report Summary
  • [Publications] 太田有三: "凸多面体リアプノフ関数の不連続系への応用について" システム制御情報学会論文誌. 7. 228-230 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Y.Ohta: "Computer Genaration of Lyapunov Function and Estimate of a Stability Region" Electronics and Communications in Japan,part3 : Fundamental Electronic Science. 77. 44-54 (1994)

    • Related Report
      1994 Annual Research Report
  • [Publications] Y.Ohta: "Computer generalized Lyapunov functions for a class of nonlinear systems" IEEE Trans.on Circuits and Systems-I. 40. 343-354 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 太田有三: "リヤプノフ関数の自動生成と安定領域の推定" 電子情報通信学会論文誌A. J76-A. 1286-1293 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] 太田有三: "凸多面体リアプノフ関数と動的凸包算法" システム制御情報学会誌. 38 (掲載予定). (1994)

    • Related Report
      1993 Annual Research Report

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Published: 1993-04-01   Modified: 2016-04-21  

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