非线性电路平衡点全局渐近稳定的特征值-范数判据

Matrix Norms-eigenvalues Theorems for the Global Aymptotic Stability of the Equilibrium Point of Nonlinear Circuit

提出了一种新的分析非线性电路平衡点全局渐近稳定的方法．新方法以矩阵范数及特征值为工具，结合平衡点的渐近稳定判据，用一个矩阵的范数及特征值的不等式决定平衡点的全局渐近稳定性．与目前该问题所采用的 Ｌｙａｐｕｎｏｖ直接法相比，新方法具有无须判断平衡点的惟一性，判别方程直接明了．同时，新方法对于其它形式非线性系统的分析，也有重要的启发性及应用价值．

In this paper, 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 inequalities of the some matrixes norms and measures. By the method in this paper, 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 Lyapunov 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.