具有分解形式的高维滞环多值电路唯一稳态研究

利用矩阵分解方法，在用常数界定元件成份关系斜率条件下，得到了确定高维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，可以用分解矩阵的稳定性来决定。结果中，电路元件可以是多值的。这大大放松了目前已有的经典结果中要求电路元件为单值的限制，扩展了已有的结果。同时，对于确定高维非线性自治电路的唯一稳态，比已有结果更加有力和简洁。

On the Uniqueness of the Steady State of the Nonlinear Nonautonomous Circuits with Hysteresis Loop Elements in Decomposition Forms

Under the conditions where the slopes of the elements' constitutive relations are expressed by constant intervals, a new criterion for the unique steady state of the nonlinear nonautonomous circuits with hysteresis elements in decomposition is obtained by matrix measures and norms. The main results obtained in this paper show that the unique steady state of the nonlinear nonautonomous circuits can be determined by the stability of decomposed matrixes. The restriction to the elements of circuits is just that the slope of the constitutive relation is bounded, much looser than the demands put forward by previously published papers. The new criteria in this paper have much wider applicable range than the results already known.