Local Representation of Nonlinear Control Systems on Kahler Manifold

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