基于矩阵测度的时变非线性非自治电路唯一稳态研究

Matrix measure and its application to determining the unique steady state of the nonlinear circuits with general time varying resistors, inductors and capacitors

对非线性非自治电路 (系统 )唯一稳态的已有研究结果表明 ,如果电路中元件的成分关系是非时变的并且是严格递增的 (即斜率为正 ) ,则对于不同的电路可以得到不同的保证电路具有唯一稳态的条件。然而对于电路元件为时变的情况 ,目前还没有相应的结果。本文利用矩阵测度的相关方法 ,第一次得到了确定时变非线性非自治电路唯一稳态的条件。结果表明 ,时变非线性非自治电路的唯一稳态 ,可以用一个矩阵测度来决定。这大大放松了目前已有的经典结果中要求电路元件为非时变的限制 ,扩展了已有的结果。

The previous research result shows that if the nonlinear nonautonatious circuit contains non-variant and stritly-increasing elements,different conditions for the uniqueness of the steady state of the circuit can be obtained.In this paper,the uniqueness of the steady state of the circuits with general time varying elements is analyzed by matrix measure. The results obtained in this paper show that the unique steady state of those kinds of time varying circuits can be determined by the measure of some matrixes. Because many restraints for the elements in the previously published are canceled,the conclusions of this paper have much wider applicable range than the results already known.