| 具有分解形式的高维非线性电路平衡点全局渐近稳定的研究 |
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| 引用本文： | 冯平. 具有分解形式的高维非线性电路平衡点全局渐近稳定的研究[J]. 青岛大学学报(工程技术版), 2001, 16(1): 11-15 |
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| 作者姓名： | 冯平 |
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| 作者单位： | 解放军后勤工程学院电工教研室, |
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| 基金项目： | 军队科研基金 !(营 160号 )资助 |
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| 摘 要： | 提出了一种新的分析具有分解不甘落后 高维非线性电路平衡点全局渐近稳定的方法。这种方法以矩阵分解为工具，结合平衡点的渐进稳定判据，用分解矩阵的稳定性决定平衡点的全局渐近稳定性。与目前该问题所采用的LIYAPUNOV直接法相比，该方法具有无须判断平衡点的唯一性，判别方程直接明了等优点，电路维数越大时，本文的方法越有其优势。同时，该方法对于其他形式的非线性系统的分析，也有重要的启发性及应用价值。
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| 关 键 词： | 非线性电路 唯一稳态 平衡点 矩阵分解 全局渐近稳定性 LIYAPUNOV直接法 |
| 文章编号： | 1006-9798(2001)01-0011-05 |
| 修稿时间： | 2000-10-24 |
MATRIX DECOMPOSITION THEOREMS FOR THE GLOBAL AYMPTOTIC STABILITY OF THE EQUILIBRIUM POINT OF NONLINEAR CIRCUIT |
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| Feng Ping. MATRIX DECOMPOSITION THEOREMS FOR THE GLOBAL AYMPTOTIC STABILITY OF THE EQUILIBRIUM POINT OF NONLINEAR CIRCUIT[J]. Journal of Qingdao University(Engineering & Technology Edition), 2001, 16(1): 11-15 |
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| Authors: | Feng Ping |
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| Abstract: | A new method to analyze the global asymptotic stability of the equilibrium point of nonlinear circuit is introduced. The conditions for the global asymptotic stability of the equilibrium point are expressed as the stability of the some decomposed matrix. By the method in this paper, for deciding the global asymptotic stability of the equilibrium point, it is not necessary to verify whether the equilibrium point is unique and to construct Liyapunov functions. And the requirements in the conditions for the circuit elements are only their slopes being bounded, which are much loose than those in previous papers. So this work is an extension for the classical results already known. |
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| Keywords: | nonlinear circuit matrix decomposition global asymptotic stability equilibrium point |
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