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| 线性控制系统的无界多面体不变集 | |
| 引用本文： | 张霞,高岩,夏尊铨.线性控制系统的无界多面体不变集[J].控制理论与应用,2011,28(6):874-880. |
| 作者姓名： | 张霞 高岩 夏尊铨 |
| 作者单位： | 1. 大连理工大学数学科学学院,辽宁大连116024;浙江财经学院数学与统计学院,浙江杭州310018 2. 上海理工大学管理学院,上海,200093 3. 大连理工大学数学科学学院,辽宁大连,116024 |
| 基金项目： | 国家自然科学基金资助项目(10671126, 10971187, 11071029); 上海市重点学科建设资助项目(S30501); 上海市科委地方高校能力建设资助项目(10550500800); 安徽省高等学校省级自然科学研究资助项目(KJ2010B102). |
| 摘 要： | 本文利用非光滑分析方法,讨论了线性控制系统的无界多面体不变集问题.当无界多面体的极方向满足一定条件时,得到了该无界多面体为一类线性控制系统弱不变集的判别方法.然后在更一般的线性控制系统下给出了无界多面体为强不变集的充分条件.最后给出两个应用实例. |
| 关 键 词： | 线性控制系统 不变集 多面体 非光滑分析 |
| 收稿时间： | 2009/4/24 0:00:00 |
| 修稿时间： | 6/6/2010 12:00:00 AM |
Unbounded polyhedral invariant sets for linear control systems |
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| ZHANG Xi,GAO Yan and XIA Zun-quan.Unbounded polyhedral invariant sets for linear control systems[J].Control Theory & Applications,2011,28(6):874-880. | |
| Authors: | ZHANG Xi GAO Yan and XIA Zun-quan |
| Affiliation: | School of Mathematical Sciences, Dalian University of Technology; School of Mathematics and Statistics, Zhejiang University of Finance and Economics,School of Management, University of Shanghai for Science and Technology,School of Mathematical Sciences, Dalian University of Technology |
| Abstract: | The nonsmooth analysis methods are applied to investigate the unbounded polyhedral invariant sets for linear control systems. When the extreme directions of an unbounded polyhedron satisfy some conditions, we derive the criterion for that unbounded polyhedron to be a weak invariant set for a class of linear control systems. The sufficient condition is also obtained for the unbounded polyhedron to be the strong invariant set for more general linear control systems. Two applied examples are given for illustration. |
| Keywords: | linear control systems invariant set polyhedron nonsmooth analysis |
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