高维非线性电路平衡点稳定性研究

提出了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,结合平衡点的渐近稳定判据,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,判别方法直接明了等优点.电路维数越大时,此方法越有其优势.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.

Study of Stability of Higher-Dimension Non-Linear Circuit Equilibrium Point

In the paper, puts forward a new method to analyze the progressive stability of higher- dimension non-linear circuit equilibrium point. This method takes the matrix resolving as a tool, combined with criterion of progressive stability and determines the equilibrium point by stability of matrix resolving. Compared with the current LIYAPUNOV method, this one has many advan- tages: it is not necessary to judge uniqueness of the equilibrium point; it is direct; and while the dimension number is higher, the method is more useful. At the same time, this method is valuable and illuminative for analyzing other non-linear system.