| 线性多变量系统的控制Lyapunov函数构造 |
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| 引用本文： | 蔡秀珊,韩正之,吕干云,王 霄.线性多变量系统的控制Lyapunov函数构造[J].控制理论与应用,2009,26(1):46-50. |
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| 作者姓名： | 蔡秀珊 韩正之 吕干云 王 霄 |
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| 作者单位： | 1. 浙江师范大学数理与信息工程学院,浙江,金华321004
2. 上海交通人学自动化系,上海,200030 |
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| 基金项目： | 国家自然科学基金资助项目(60774011); 浙江省自然科学基金资助项目(Y105141). |
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| 摘 要： | 提出线性多变量系统控制Lyapunov函数(CLF)构造的一般方法. 先证明可以通过解一类Lyapunov方程, 得到线性系统二次型的CLF. 接着证明了对于线性系统, 这种方法可以提供所有二次型的CLF. 最后证明了若线性系统存在CLF, 那么必存在二次型的CLF. 由此完全解决了线性系统的CLF构造问题.
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| 关 键 词： | 线性系统 控制Lyapunov函数 Yokoyama标准形 反馈镇定 |
| 收稿时间： | 2006/12/3 0:00:00 |
| 修稿时间： | 2007/11/10 0:00:00 |
The construction of control Lyapunov functions for linear multivariable systems |
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| CAI Xiu-shan,HAN Zheng-zhi,L?U Gan-yun and WANG Xiao.The construction of control Lyapunov functions for linear multivariable systems[J].Control Theory & Applications,2009,26(1):46-50. |
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| Authors: | CAI Xiu-shan HAN Zheng-zhi L?U Gan-yun and WANG Xiao |
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| Affiliation: | College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua Zhejiang 321004, China;Department of Automation, Shanghai Jiaotong University, Shanghai 200030, China;College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua Zhejiang 321004, China;College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua Zhejiang 321004, China |
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| Abstract: | A universal method for constructing control Lyapunov functions (CLF) for a linear multivariable system is presented. Firstly, we show that every quadratic control Lyapunov function can be obtained by solving the Lyapunov equation. Then, we prove that this method can generate all quadratic control Lyapunov functions for a given linear system. Finally, it is shown that if there is a control Lyapunov function then there must be a quadratic control Lyapunov function. Thus, the problem of constructing control Lyapunov functions for linear systems is solved completely. |
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| Keywords: | linear systems control Lyapunov functions Yokoyama canonical form feedback stabilization |
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