基于圆判据的一种LMI绝对镇定方法

杨莹; 黄琳

基于圆判据的一种LMI绝对镇定方法

杨莹,
黄琳

北京大学力学与工程科学系系统与控制研究中心, 北京 100871

基金项目: 国家自然科学基金资助项目(10272001);国家重点基础研究专项经费资助项目G1998020302)

详细信息

作者简介:
杨莹(1973),女,河南人,博士(E-mail:yy@mech.pku.edu.cn).

中图分类号: TP273
计量
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- 被引次数: 0
出版历程
- 收稿日期: 2001-03-19
- 修回日期: 2003-04-29
- 刊出日期: 2003-08-15

Absolute Stabilization Related to Circle Criterion: an LMI-Based Approach

Center for Systems and Control, Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P. R. China

摘要

摘要: 针对非线性Lur'e系统,提出了一种输出反馈控制器综合方法。对于系统在无摄动及线性部分存在乘性范数摄动的情况,分别设计了保证闭环系统绝对稳定的动态输出反馈控制器。由圆判据出发,通过把绝对稳定性问题等价地转化成H∞控制问题,得到了一组由线性矩阵不等式(LMI)表达的控制器存在的充分性条件。
- 非线性Lur’e系统 /
- 圆判据 /
- 绝对稳定性 /
- H∞控制 /
- LMI
Abstract: Amethod is proposed for synthesizing output feedback controllers for nonlinear Lur'e systems.The problem of designing an output dynamic controller for uncertain-free systems and systems subject to multiplicative norm-bounded perturbations in the linear part were proposed respectively.The procedure is based on the use of the absolute stability,through the circle criterion,and a linear matrix inequalities(LMI) formulation.The controller existence conditions are given in terms of existence of suitable solutions to a set of parameter-dependent LMIs.
- nonlinear Lur’e systems /
- circle criterion /
- absolute stabilization /
- H_∞ control /
- LMI

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参考文献(12)

[1]	Lur'e A I,Postnikov V N.On the theory of stability of control systems[J].Prikl Mat Meh,1944,8(3).
[2]	Popov V.Absolute stability of non-linear systems of automatic control[J].Automation and Remote Control,1961,22:857-875.
[3]	Narendra K S,Taylor J H.Frequency Domain Criteria for Absolute Stability[M].New York:Academic Press,1973.
[4]	Vidyasagar M.Nonlinear System Analysis[M].Englewood Cliffs,NJ:Prentice Hall,1993.
[5]	Khalil H K.Nonlinear System[M].New York:MacMillan Pubishing,1992.
[6]	Boyd S,Chaoui L E,Feron E,et al.Linear Matrix Inequalities in System and Control Theory[M].Philadelphia,Pennsylvania:SIAM,1994.
[7]	Savkin A V,Petersen I R.A connection between H∞ control and the absolute stabilizability of uncertain systems[J].System and Control Letters,1994,23(3):197-203.
[8]	Konishi K,Kokame H.Robust stability of Lur'e systems with time-varying uncertainties:a linear matrix inequality approach[J].Int J Systmes Science,1999,30(1):3-9.
[9]	Kahutani Y,Hagiwara T,Araki M.LMI representation of the shifted of Popov criterion[J].Automatica,2000,36(5):765-770.
[10]	Gahinet P,Arkadi Nemirovski,Laub J A,et al.LMI Control Toolbox User's Guide[M].Natick,Mass:The Math Works,Inc,1995.
[11]	Iwasaki,Skelton R E.All controllers for the general H∞ control problem:LMI existence conditions and state space formulas[J].Automatica,1994,30(8):1307-1317.
[12]	Izumi Masubuchi,Atsumi Ohara,Nobuhide Suda.LMI-based controller synthesis:a unified formulation and solution[J].Int J Robust Nonlinear Control,1998,8(8):669-686.