Parameter Space Stability Analysis Revisited : Kharitonov-Type Theorems and Their Application

重温参数空间稳定性分析：Kharitonov 型定理及其应用

• 批准号: 01550332
• 负责人: MORI Takehiro
• 金额: $ 1.22万
• 依托单位: Kyoto Institute of Technology (1990)Kyoto University (1989)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1989
• 资助国家: 日本
• 起止时间: 1989 至 1990
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-01550332/
• 关键词: Stability analysis; Parameter space; Robust stability; Kharitonov's theorem; カリトノフ定理

1. Studies were made on conditions for a polytope of matrices to belong to P- (M-) matrices, matrix classes that have close ties to the stability analysis of control systems. Necessary and sufficient conditions for some specific situations and sufficient conditions for a general case are derived.2. An answer is given to the problem on characterization of the class of systems that maintain stability under additive parameter perturbations. The employed method is the Lyapunov's second method. Some illustrative examples are worked out.3. Stability is studied for interval polynomials with vanishing extreme coefficients. It is found that Kharitonov's theorem almost remains valid even in this situation.4. Aperiodicity and periodicity of interval polynomials are investigated and exact conditions for them are given. It is claimed that we have only to check two extreme polynomials.

1.研究了与控制系统稳定性分析密切相关的矩阵类P-（M-）矩阵的多胞形的判定条件。给出了一些特殊情况下的充要条件和一般情况下的充分条件.给出了在附加参数扰动下保持稳定的系统的特征问题的一个答案。所采用的方法是李雅普诺夫第二方法。并给出了一些说明性的例子.研究了极值系数为零的区间多项式的稳定性。发现即使在这种情况下，Kharitonov定理几乎仍然有效.研究了区间多项式的非周期性和周期性，给出了它们存在的充分条件。它声称，我们只需要检查两个极端的多项式。

项目成果

森 武宏: "行列ポリト-プがP(M)行列である条件" 電気学会論文誌. 100ーC. 273-278 (1990)

Takehiro Mori：“矩阵多面体成为 P(M) 矩阵的条件”，日本电气工程师学会汇刊 100-C 273-278 (1990)。

T. Mori: "Stability of interval polynomials with vanishing extreme coefficients : validity of Kharitonov's theorem" Trans. ISCIE. Vol. 3. 335-337 (1990)

T. Mori：“极值系数消失的区间多项式的稳定性：哈里托诺夫定理的有效性” Trans。

Takehiro Mori: "Aperiodicity and periodicity of interval polynowials" Proc.of the 1990 Conference on Decision & Control. 39-40 (1990)

Takehiro Mori：“区间多项式的非周期性和周期性”Proc.of 1990 Conference on Decision

森 武宏: "2次形式リヤプノフ関数を共有する線形連続時間システムの特徴づけ" 電子情報通信学会論文誌. J72ーA. 1520-1522 (1990)

Takehiro Mori：“共享二次 Lyapunov 函数的线性连续时间系统的特性”，电子、信息和通信工程师学会汇刊 J72-1522 (1990)。

T. Mori: "Characterization of linear continuous time systems with a common quadratic Lyapunov function" Trans. IEICE. Vol. J-73A. 1520-1522 (1990)

T. Mori：“具有常见二次李亚普诺夫函数的线性连续时间系统的表征”Trans。