基于矩阵测度的非线性非自治电路惟一稳态研究

A Study on the Unique Steady State of a Nonlinear Nonautonomous Circuit Based on Matrix Measure

以矩阵测度为工具 ,得到了确定非线性非自治电路惟一稳态的新条件 .结果表明 :非线性非自治电路的惟一稳态 ,可以用一个矩阵的测度来决定 .该结果对电路元件的约束 ,仅要求其斜率有界即可 ,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 。

A new criterion to the unique steady state of a nonlinear nonautonomous circuit is obtained by matrix measure method. The main results obtained in this paper show that the unique steady state of the nonlinear nonautonomous circuit can be determined by the measure of a matrix. The requirement of the criterion to the elements of the circuit is that the slopes of their constitutive relations are bounded, and the requirement is much more lenient than that of the classical criterions. The new criterion has much wider applications than the previous ones.