Construction of ParameterDependent Lyapunov Functions for Robust Control
Project/Area Number  05650393 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
計測・制御工学

Research Institution  Kyoto Institute of Technology 
Principal Investigator 
MORI Takehiro Kyoto Institute of Technology, Dept. of Electro. & Inf. Sci., Professor, 工芸学部, 教授 (60026359)

CoInvestigator(Kenkyūbuntansha) 
KUROE Yasuaki Kyoto Institute of Technology, Dept. of Electro. & Inf. Sci., Associate Professo, 工芸学部, 助教授 (10153397)

Project Fiscal Year 
1993 – 1994

Project Status 
Completed(Fiscal Year 1994)

Budget Amount *help 
¥2,200,000 (Direct Cost : ¥2,200,000)
Fiscal Year 1994 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1993 : ¥1,700,000 (Direct Cost : ¥1,700,000)

Keywords  Lyapunov function / Parameterdependence / Robust stability / Polytope of polynomials / Quadratic form / Discrete systems / Common Lyapunov function / リヤプノフ関数 / パラメータ依存 / ロバスト安定性 / 多項式ポリトープ / 二次形式 / 離散時間システム / 共通リヤプノフ関数 / エルミート行列 
Research Abstract 
1) In the first year of the project term, investigations were on ways to construct Lyapunov functions for linear systems represented by polynomials with uncertain coefficient parameters. This leads to an expected result that there actually exist a parameterdependent Lyapunov function for the given polytopic uncertain polynomial. The Lyapunov function is also a polytope of Lyapunov functions that correspond to the extreme polynomials of the polytope of polynomials. We see a onetoone correspondence between parameters of Lyapunov functions and those of polynomials. 2) With this result, we then pass to uncertain nonlinear systems, anticipating some parallel results with the linear case. Deliberation together with numerical experiences, however, led us to conclude that for nonlinear systems seach for parameterdependent Lyapunov functions was harder than expected. We were thus obliged to reconsider our idea and began to look for the "oppositeend" problem, socalled common Lyapunov function problem. This is because common Lyapunov functions for several systems make us easy to handle uncertain nonlinear systems. 3) In the final year, we set out to consider this problem for linear systems in the first place. We could successfully identify some classes of discertetime linear systems that have common quadratic Lyapunov functions. This yields a sufficient condition for the This could also give a scope to explore results for uncertain nonlinear systems Lyapunof function approach.

Report
(4results)
Research Output
(9results)