滞环多值电路唯一稳态的范数判据

Norm Theorems for the Unique Steady State of the Nonlinear Nonautonomous Circuits with Hysteresis Loop Elements

以矩阵范数为工具,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。本文的结果表明,该类电路的唯一稳态,可以用矩阵的范数来决定。本文的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,扩展了已有的结果。

A new criterion to the unique steady state of the nonlinear nonautonomous circuits with hysteresis elements is obtained by matrix norms . The main results obtained in this paper show that the unique steady state of the nonlinear nonautonomous circuits can be determined by the norms 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 in this paper have much wider applicable range than the results already known.