中文摘要：

利用非线性控制系统的几何理论,研究了建立在Hermite流形上的非线性控制系统,给出了Hermite流形上的非线性控制系统的局部表示。利用微分几何测地线的性质,研究了非线性控制系统的平衡态与Hermite流形上的测地线之间的关系,讨论了建立在Hermite流形上的非线性控制系统的局部能控和局部能观测性,证明了建立在Hermite流形上的非线性控制系统是局部能控和局部能观测的。

英文摘要：

The nonlinear control system on Hermite manifold is studied by using differential geometric theory of nonlinear control system. The local representation of the state equation of nonlinear control systems on the coordinate of Hermite manifold is given. By using the property of geodesic the relationship between equilibrium of nonlinear systems and geodesic of Hermite manifold considered. At last, the local controllability and local observability of nonlinear systems on Hermite manifold are studied. It is proved that the system on Hermite manifold is controllable and observable.