线性非时变系统状态空间分析新方法

A new method for state space analysis of linear time-invariant systems

提出了求解线性非时变状态方程的新公式 .新公式具有矩阵 -向量形式 ,对于线性连续和离散系统 ,其全响应都可分解为强制响应和自由响应 ,使得系统动态方程的解法更加完整 ,其中强制响应作为讨论的重点 .在一阶电路中新公式与常规的三要素公式相一致 .新的三要素公式特别适用于常量、指数或正弦激励信号的情况 。

Presents new vector matrix form formulas for solving linear time invariant state equations. The responses of linear continuous and discrete systems may be decomposed into force responses and free responses. The force responses are discussed in detail. For first order circuits the new formula is similar to ordinary three element formula. The new three element formula is suitable for solving state equations of which the exciting functions are constants, exponential functions, or sinusoidal functions etc. Some formulas are given for solving the above state equations. The new formula can be used to solve state equations to distinguish stable and free responses.