非线性电路平衡点全局渐近稳定的λ参数法  

The study of the global aymptotic stability of the equilibrium point of nonlinear circuits by λ-coefficient meyhod

作　　者：刘万松[1] 冯平[2] 

机构地区：[1]贵州师范大学物理与电子科学系,贵州贵阳550001 [2]解放军后勤工程学院电工教研室,重庆400016

出　　处：《黔东南民族师范高等专科学校学报》2002年第3期6-9,共4页Journal of Southeast Guizhou National Teachers College

摘　　要：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 .这种方法以元件成分关系斜率变化区间对应的常数矩阵为基础 ,通过引入一个参变量λ构造出多个新的矩阵 .通过对这些包含参变量λ的矩阵分析 ,结合平衡点的渐近稳定判据 ,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惟一性 ,判别方程直接明了等优点 .同时 ,该方法对于其他形式的非线性系统的分析 。In this paper,based on the constant matrixes composed of the constant intervals of the slopes of the elements' constitutive relations,a coefficient λ is introduced to construct several new matrixes relative to this coefficient.By means of the analysis of those matrixes,a new method to analyze the global asymptotic stability of the equilibrium point of nonlinear circuit is advanced.The conditions for the global asymptotic stability of the equilibrium point are expressed as the inequalities of the some matrixes norms and measures including the coefficient.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 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.

关 键 词：非线性电路 平衡点 全局渐进稳定 Λ参数法 数字模拟 

分 类 号：TM132[电气工程—电工理论与新技术]