非线性电路平衡点全局渐近稳定性研究

Study on the Global Asymptotic Stability of the Equilibrium Point for Nonlinear Circuits

对具有分解形式高维非线性电路平衡点全局渐近稳定性分析提出一种新方法 .此法以矩阵分解为工具 ,在用常数界定元件成分关系斜率条件下 ,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 ,与目前解决该问题所采用的LIYAPUNOV直接法相比 ,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 ,其优势越明显 .同时 ,对其他形式非线性系统的分析也有启发及应用价值 .

In this paper, on condition when the slopes of the elements' constitutive relations are bounded by some given constants, a new method is introduced to analyze the global asymptotic stability of the equilibrium point for nonlinear circuits. The conditions for the global asymptotic stability of the equilibrium point are determined by stability of certain decomposed matrices. By using this method to decide the global asymptotic stability of the equilibrium point, it is not necessary to verify the uniqueness of the equilibrium point or to contrast Liyapunov functions. And the requirements in the conditions for the circuit elements are only such, as their slopes are bounded, which is much weaker than those published in previously papers. The method in this paper has its obvious advantage,especially when the dimension of circuit becomes larger and larger. Furthermore,this method is full of enlightenment and applicable to the analysis of other types of nonlinear systems.