Solution to the Common Lyapunov-Function Problem via Fusion of Numerical and thalytical Aspec

通过数值和数学 Aspec 的融合解决常见的 Lyapunov 函数问题

• 批准号: 07650489
• 负责人: MORI Takehiro
• 金额: $ 1.41万
• 依托单位: Kyoto Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07650489/
• 关键词: common Lyapunov function; quadratic Lyapunov fuction; continuous-time systems; discrete-time systems; LMI; リヤプノフ関数; ロバスト安定性; 線形行列不等式; 数値解法; 解析解法; 二次形式

1. We first tested several methods available to solve LMI,into which the common Lyapunov function problem can be recast, and found the so-called interior-point method most suitable for the present purpose. Based on this method, we developed a computation code by ourselves and used it throughout the study.2. With knowledge or experience attained in the above computation process, we are successful in finding some subclasses of systems, continuous-time or discrete-time, that have a quadratic Lyapunov function in common. Some subclasses for low-order systems have also been found. In general, we noticed, there exists a parallel between continuous-time case and discrete-time one. This would give a further insight into the problem.3. Since there exists a close connection between the problem in question and the quadratic stability problem of systems, we looked into the quadratic stability property of interval polynomials and obtained some results.

1.我们首先测试了几种方法可用于解决线性矩阵不等式，其中常见的李雅普诺夫函数的问题，可以重铸，并发现所谓的邻居点方法最适合目前的目的。在此基础上，我们自行编制了计算程序，并在整个研究过程中使用.在上述计算过程中获得的知识或经验，我们成功地找到一些子类的系统，连续时间或离散时间，有一个共同的二次李雅普诺夫函数。一般来说，我们注意到，连续时间系统和离散时间系统之间存在着一种平行关系。这将使我们对这个问题有更深入的了解.由于该问题与系统的二次稳定性问题有着密切的联系，本文研究了区间多项式的二次稳定性，得到了一些结果。

项目成果

Y.Mori et al.: "A Partial Solution to the common Lyapunov function problem ; continuous-time case" Proc.of ICARCV '96. 1064-1068 (1996)

Y.Mori 等人：“常见 Lyapunov 函数问题的部分解决方案；连续时间情况”Proc.of ICARCV 96。

Y. Mori: "A Partial Solution to the Common Lyapunov Function Problem : Continuous-Time Case" Proc. of ICARCV'96. 1064-1068 (1996)

Y. Mori：“常见 Lyapunov 函数问题的部分解决方案：连续时间情况”Proc。

森禎弘: "不確かな離散時間線形システムの二次安定性と安定化" 電気学会論文誌・C. 115-C. 1291-1296 (1995)

Yoshihiro Mori：“不确定离散时间线性系统的二次稳定性和稳定性”，日本电气工程师协会会刊，C. 115-C. 1291-1296 (1995)

Yoshihiro Mori: "Coosses of Discrcte Linear Systems Having Common Quadratic" Proc of 1995 American Control Confeuce. 3364-3365 (1995)

Yoshihiro Mori：“具有公共二次方的离散线性系统的 Coosses”Proc，1995 年 American Control Confeuce。

Y.Mori et al.: "Quadratic stability and stabilization of uncertain discrete-time linear systems" Trans.IEEJ. Vol.115-C. 1291-1296 (1995)

Y.Mori 等人：“不确定离散时间线性系统的二次稳定性和稳定性” Trans.IEEJ。