具有分解形式的高维非线性电路唯一稳态研究

利用矩阵分解方法，得到了确定高维非线性非自治电路唯一稳态的新条件。结果表明，非线性非自治电路的唯一稳态，可以用分解矩阵的稳定性来决定。结果对电路元件的约束，仅要求其成份关系斜率有界即可。这大大放松了目前已有的经典结果中要求电路元件斜率为正的限制，扩展了已有的结果。本文的结果，对于确定高维非线性非自治电路的唯一稳态，比已有方法更加有力和简洁。

Study on the uniqueness of the steady state of the high degrees nonlinear nonautonomous circuits in decomposition form

A new criterion to the unique steady state of the nonlinear nonautonomous circuits in decomposition forms is obtained ,which are expressed by the stability of the decomposed matrixes. The restriction to the elements of circuits is just the slope of the constitutive relation is bounded, which is much looser than the demands put forward by previously published papers. The new criterions have much wider applicable range than the results already known.