| 摄动离散矩阵Lyapunov方程解的估计 |
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| 引用本文： | 陈东彦,侯玲.摄动离散矩阵Lyapunov方程解的估计[J].控制理论与应用,2006,23(5):830-832. |
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| 作者姓名： | 陈东彦 侯玲 |
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| 作者单位： | 哈尔滨理工大学,应用数学系,黑龙江,哈尔滨,150080;哈尔滨理工大学,应用数学系,黑龙江,哈尔滨,150080 |
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| 基金项目： | 国家自然科学基金资助项目(10471031)． |
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| 摘 要： | 研究摄动离散矩阵Lyapunov方程解的估计问题,利用矩阵运算性质及Lyapunov稳定性理论,给出在结构不确定性假设下方程解的存在条件及解的上下界估计,估计结果由一个线性矩阵不等式(LMI)和两个矩阵代数Riccati方程确定．针对几种不确定性假设,进一步给出矩阵代数Riccati方程的具体形式．最后通过一个算例说明了所得结果的有效性．
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| 关 键 词： | 离散矩阵Lyapunov方程 不确定性 矩阵代数Riccati方程 线性矩阵不等式 |
| 文章编号： | 1000-8152（2006）05-0830-03 |
| 收稿时间： | 5/8/2005 12:00:00 AM |
| 修稿时间： | 2005-05-082005-11-29 |
On the estimation of solutions to perturbed discrete matrix Lvapunov equations |
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| CHEN Dong-yan,HOU Ling.On the estimation of solutions to perturbed discrete matrix Lvapunov equations[J].Control Theory & Applications,2006,23(5):830-832. |
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| Authors: | CHEN Dong-yan HOU Ling |
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| Affiliation: | Department of Application Mathematic, Harbin University of Science and Technology, Harbin Heilongjiang 150080, China |
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| Abstract: | The estimation of the solution to the perturbed discrete matrix Lyapunov equation is studied. The existence condition and upper and lower bounds estimation of the solution to the equation under the structured uncertainty assumption are presented by applying the operational property of matrix and Lyapunov stability theory, the estimation is then determined by a linear matrix inequality (LMI) and two matrix algebra Riccati equations. The concrete form of matrix algebra Riccati equations are also given for some uncertainty assumptions. Finally, the effectiveness of above results is shown by an example. |
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| Keywords: | discrete matrix Lyapunov equation uncertainty matrix algebra Riccati equation linear matrix inequality |
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