Computer Generation of Lyapunov Functions and Its Applications
| Project/Area Number |
05650371
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
System engineering
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| Research Institution | Kobe University |
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Principal Investigator |
HANEDA Hiromasa Kobe University, Dept.of Elec.& Electr.Eng., Professor, 工学部, 教授 (10031113)
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| 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)
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| Project Period (FY) |
1993 – 1994
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| Project Status |
Completed (Fiscal Year 1994)
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| 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)
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| Keywords | Lyapunov 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 |
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| 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.
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Report
(3 results)
Research Products
(15 results)
