利用单位解矩阵估计判定滞环多值电路唯一稳态

The Determination of the Unique Steady State of the Nonlinear Nonautonomous Circuits with Hysteresis Loop Element by the Estimation of the Fundamental Solutions Matrixes

利用微分方程单位解矩阵估计的相关方法，得到了确定具有滞环的非线性非自治电路唯一稳态的新条件。结果表明，该类电路的唯一稳态可以用矩阵的测度来决定．对电路元件的约束仅要求其斜率有界即可。这大大放松了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。

Based on the estimation of the fundamental solutions matrixes of differential equations, this paper obtains a new criterion to the unique steady state of the nonlinear nonautonomous circuits with hysteresis elements by matrix measures.The main results show that the unique steady state of the nonlinear nonautonomous circuits, can be determined by the measures of some 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.