高维非线性电路平衡点全局渐近稳定的研究

提出一种新的分析具有分解形式的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，在用常数界定元件成份关系斜率条件下,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.

The study of the global asymptotic stability of the equilibrium point of nonlinear circuit

In this paper, on the conditions where the slopes of the elements' constitutive relations are expressed by constant intervals, 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 matrixes, namely, the combination of the criterion of the asymptotic stability of the e. p. and that of uniqueness of steacly state of the network. By the introduced method, to decide 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 be bounded, which are much loose than those in previously published papers. So the work of this paper is an extension for the classical results already known.