一类不确定线性周期离散时间系统的分析与控制

孙凯; 谢广明

一类不确定线性周期离散时间系统的分析与控制

孙凯¹,
谢广明^1,2

1.
北京大学工学院系统与控制中心,北京 100871;2.华东交通大学电气与电子工程学院,南昌 330013

基金项目: 国家自然科学基金资助项目(60774089;60404001)

详细信息

作者简介:
孙凯(1984- ),男,硕士生(E-mail:sunkaiflorence@gmail.com);谢广明,男(联系人.Tel:+86-10-62754083).

中图分类号: TP13；TP273；O317
计量
- 文章访问数: 2549
- HTML全文浏览量: 136
- PDF下载量: 725
- 被引次数: 0
出版历程
- 收稿日期: 2008-06-05
- 修回日期: 2009-01-03
- 刊出日期: 2009-04-15

Analysis and Control of a Class of Uncertain Linear Periodic Discrete-Time Systems

SUN Kai¹,
XIE Guang-ming^1,2

1.
LTCS, Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, P. R. China;

摘要

摘要: 讨论具有参数区间不确定性的线性周期离散时间系统的反馈控制问题．首先进行系统的鲁棒稳定性分析和镇定研究，分别给出了基于线性矩阵不等式的系统渐近稳定和状态反馈镇定的条件．接着研究系统的L2-增益分析和控制综合问题．对于L2-增益分析问题，得到一个基于线性矩阵不等式的条件，在该条件下，具有参数不确定性的线性周期自治系统渐近稳定，且有小于γ的L2-增益．对于控制综合问题，导出基于线性不等式的条件，由该条件可以得到一个状态反馈器，使得闭环系统渐近稳定，且有小于γ的L2-增益．所有这些条件都是充分必要的．
- 线性周期系统 /
- 参数不确定性 /
- 鲁棒稳定性 /
- 线性矩阵不等式 /
- 状态反馈 /
- 镇定 /
- L[KG3]2-增益
Abstract: Feedback control problems for linear periodic systems (LPSs) with interva-l type parameter uncertainties are studied in the discrete-time domain.First,the stability analysis and stabilization problems were addressed.Conditions based on linear matrices inequality for asymptotical stability and state feedback stabilization respectively were given.Problems of B2-gain analysis and control synthesis problems were studied.For the B2-gain analysis problem,an LMI-based condition was obtained such that the autonomous uncertain LPS is asymptotically stable and has an B2-gain smaller than a positive scalar gamma.For the control synthesis problem,an LM-Ibased condition was derived to build a state feedback controller ensuring the closed-loop system is asymptotically stable and has an B2-gain smaller than a positive scalar gamma.All the conditions are necessary and sufficient.
- linear periodic system /
- parameter uncertainty /
- robust stability /
- linear matrix inequality (LMI) /
- state feedback /
- stabilization /
- B2-gain

HTML全文

参考文献(15)

[1]	Bittanti S. Deterministic and stochastic linear periodic systems[A].In:Bittanti S,Ed.Time Series and Linear Systems[C].Berlin:Springe-Verlag, 1986, 141-182.
[2]	Bittanti S, Bolzern P, Colaneri P. Stability analysis of linear periodic systems via the Lyapunov equation[A].In:Ljung L,Strom K J,Eds.Proceedings of the 9th IFAC World Congress[C].Vol 1.Budapest, Hungary,Oxford:Pergmon Press,1984, 169-173.
[3]	Kono M. Eigenvalues assignment in linear periodic discrete-time system[J]. International Journal of Control,1980,32(1):149-158. doi: 10.1080/00207178008922850
[4]	Hernanadez V,Urbano A M. Pole-placement problem for discrete-time linear periodic systems[J].International Journal of Control,1989,50(1):361-371. doi: 10.1080/00207178908953366
[5]	Grasselli O M. Canonical decomposition of linear periodic discrete-time systems[J]. International Journal of Control,1984,40(1):201-214. doi: 10.1080/00207178408933268
[6]	Bittanti S,Bolzernm P. Stabilizability and detectability of linear periodic systems[J].Systems and Control Letters,1985,6(2):141-145. doi: 10.1016/0167-6911(85)90083-0
[7]	Bittanti S,Colaneri P,De Nicolao G. Discrete-time linear periodic systems:a note on the reachability and controllability interval length[J].Systems and Control Letters,1986,8(1)：75-78. doi: 10.1016/0167-6911(86)90033-2
[8]	Bolzern P,Colaneri P. Inertia theorems for the periodic Lyapunov difference equation and the periodic Riccati difference equation[J].Linear Algebra Appl,1987,85(1):249-265. doi: 10.1016/0024-3795(87)90221-7
[9]	Chen T,Qiu L. Linear periodically time-varying discrete-time systems:aliasing and LTI approximations[J].Systems and Control Letters,1997,30(5):225-235. doi: 10.1016/S0167-6911(97)00006-6
[10]	XIE Li-hua,de Souza C E.H∞ state estimation for linear periodic systems[J].IEEE Transactions on Automatic Control,1993,38（11）:1704-1707. doi: 10.1109/9.262045
[11]	Farges C,Peaucelle D,Arzelier D,et al.Robust H2 performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs[J].Systems and Control Letters,2007,56(2):159-166. doi: 10.1016/j.sysconle.2006.08.006
[12]	Boyd S,Ghaou L E,Feron E,et al.Linear Matrix Inequalities in Systems and Control Theory[M]. Philadelphia:SIAM,1993.
[13]	Petersen I R. A stabilization algorithm for a class of uncertain linear systems[J]. Syst Control Lett,1987,8(4):351-357. doi: 10.1016/0167-6911(87)90102-2
[14]	Khargonekar P P,Petersen I R,Zhou K. Robust stabilization of uncertain linear systems:quadratic stabilization and H∞ control theory[J].IEEE Trans Auto Control,1990,35(3):356-361. doi: 10.1109/9.50357
[15]	Skelton R E,Iwasaki T,Grigoriadis K.A Algebraic Unified Approach to Linear Control Design[M].Taylor and Francis series in Systems and Control. London：Taylor & Francis,Ltd,1998.

施引文献

资源附件(0)

访问统计

计量

文章访问数: 2549
HTML全文浏览量: 136
PDF下载量: 725
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

留言板

一类不确定线性周期离散时间系统的分析与控制

作者简介:
孙凯(1984- ),男,硕士生(E-mail:sunkaiflorence@gmail.com);谢广明,男(联系人.Tel:+86-10-62754083).

计量

Analysis and Control of a Class of Uncertain Linear Periodic Discrete-Time Systems

计量

目录

留言板

一类不确定线性周期离散时间系统的分析与控制

作者简介: 孙凯(1984- ),男,硕士生(E-mail:sunkaiflorence@gmail.com);谢广明,男(联系人.Tel:+86-10-62754083).

计量

出版历程

Analysis and Control of a Class of Uncertain Linear Periodic Discrete-Time Systems

计量

出版历程

目录

作者简介:
孙凯(1984- ),男,硕士生(E-mail:sunkaiflorence@gmail.com);谢广明,男(联系人.Tel:+86-10-62754083).