| 引用本文: | 曾建平,程 鹏,吴 斌.基于广义正交多项式的近似系统解的存在唯一性[J].控制理论与应用,2000,17(2):270~272.[点击复制] |
| ZENG Jian-ping,CHENG Peng,WU Bin.On the Existence of Unique Solution to the Approximated System Based on General Orthogonal Polynomials[J].Control Theory and Technology,2000,17(2):270~272.[点击复制] |
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| 基于广义正交多项式的近似系统解的存在唯一性 |
| On the Existence of Unique Solution to the Approximated System Based on General Orthogonal Polynomials |
| 摘要点击 1324 全文点击 963 投稿时间：1998-07-13 修订日期：1999-03-19 |
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| DOI编号 10.7641/j.issn.1000-8152.2000.2.026 |
| 2000,17(2):270-272 |
| 中文关键词 广义正交多项式 线性时变系统 近似系统 存在唯一性 |
| 英文关键词 GOPs linear time varying system approximated system existence uniqueness |
| 基金项目 博士学科点基金(9525); 国家自然科学基金(69574013)资助项目. |
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| 中文摘要 |
| 通过在投影空间中的基变换, 导出了一种基于广义正交多项式 (GOPs)展开的线性时变系统的新的近似模型. 基于这一模型, 提出了近似系统解的存在唯一性判据及其实现方案. 证明了对任意线性时变系统, 都可以构造出基于GOPs展开的近似系统, 使得对任意阶的这种近似系统的解总是存在唯一的. 最后, 给出两个简单的例子说明了本文方法的可行性. |
| 英文摘要 |
| In this paper, a new approximated model for linear time varying systems is deduced via general orthogonal polynomials(GOPs) expansion by basis transformation in projection space.Based on the model,the existence criterion of unique solution to the approximated system and its algorithm are proposed. It is shown that the approximated system via GOPs expansion can be constructed for any linear time varying system,such that there always exists a unique solution to the approximated system of any order. Finally,two simple examples are given to show feasibility of the method in this paper. |
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