定常非线性系统能控性的分析

Analysis of constant non linear system controllability

针对定常解析非线性系统进行能控性分析，采用微分方程级数解法得到状态方程的一般级数解，用作能控性分析的基本依据。用广义隐函数存在性定理为工具，结合定常解析非线性系统结构特征，分析了定理充要条件的物理意义，该充要条件与能控态点集的特征。进而得到弱能控的充要条件和能控的必要条件。对称性分析中，取得了状态转移局部对称性的充要条件。给出了能控性分析算例，表明对定常解析非线性系统能控性分析是方便有效的。

For the controllability of constant non linear system by using the progression method, the general progression solution of state equation is obtained. The solution is used as the basis of controllability analysis. With the aid of implicit function theorem, solution is simplified by using the character of analytic function. Thus the necessary and sufficient conditions of weak controllability can be obtained. The essential condition of state transform symmetry has been obtained in the symmetry analysis, and it is convenient and effective to analyzes the system controllability of constant analytic non linear system.