关于零状态、零输入以及稳态响应的线性关系的一般论证

A General Demonstration of the Linearity of Zero-State, Zero-Input and Steady-State Responses

摘要: 本文的论证分两个部分。第一部分通过状态变量法论证了线性网络的零状态响应及零输入响应的线性关系。第二部分讨论稳态响应的线性关系,在论证过程中提出了含有纯电容割集的网络及含有纯电感回路的网络为非衰减网络等几条定理,并进行了比较严谨的证明。

Abstract: The demonstration includes two steps. Firstly, the linear relationship between zero-state and zero-input responses of linear networks is demonstraped Then the linear relationship of steady state response is discussed. In the course of demonstration, several theorems are posed and proved in detail, such as networks including pure capacitance cut-sets and pure inductance loops are non-decaying, etc.