| 引用本文: | 李元龙,林宗利.奇异线性系统在执行器饱和受限下不变集条件的改进(英文)[J].控制理论与应用,2014,31(7):955~961.[点击复制] |
| LI Yuan-long,LIN Zong-li.Improved set invariance conditions for singular linear systems subject to actuator saturation[J].Control Theory and Technology,2014,31(7):955~961.[点击复制] |
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| 奇异线性系统在执行器饱和受限下不变集条件的改进(英文) |
| Improved set invariance conditions for singular linear systems subject to actuator saturation |
| 摘要点击 3038 全文点击 2057 投稿时间：2014-01-14 修订日期：2014-04-19 |
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| DOI编号 10.7641/CTA.2014.40029 |
| 2014,31(7):955-961 |
| 中文关键词 奇异系统 执行器饱和 稳定性分析 吸引域 不变集 |
| 英文关键词 singular systems actuator saturation stability analysis domain of attraction set invariance |
| 基金项目 |
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| 中文摘要 |
| 本文考虑饱和线性反馈下奇异线性系统扩大吸引域估计的问题. 根据每个输入是否饱和, 将输入空间分成 若干子区域. 在每个子区域内部, 系统模型中没有显示的部分状态的时间导数可被显式表达. 利用含有全部系统状 态的二次Lyapunov函数, 建立一组双线性矩阵不等式形式的改进的不变集条件. 该组条件下, 二次Lyapunov函数的 水平集可诱导出一个吸引域估计. 为得到最大的吸引域估计, 构建了以这些双线性矩阵不等式为约束条件的优化问 题, 并为其求解给出了迭代算法. 仿真结果表明本文得到的吸引域估计明显大于现有结果. |
| 英文摘要 |
| This paper considers the problem of enlarging the estimate for the domain of attraction of singular linear systems with saturated linear feedback. We partition the input space into several regions. In the interior of each of these regions, the time derivatives of partial states, which are not present in the system model, can be explicitly expressed. A quadratic Lyapunov function of all states of the system is employed to establish a set of conditions under which a level set of this quadratic Lyapunov function is contractively invariant with respect to the singular system, and thus results in an estimate of the domain of attraction. These conditions can be expressed in terms of bilinear matrix inequalities (BMIs). Based on these BMIs, a constrained optimization problem is formulated for obtaining the largest such estimate of the domains of attraction. An iterative algorithm is developed to solve this BMI problem. Simulation results show that the estimate thus obtained is significantly larger than an existing estimate. |