A Normal Form With Cascade Decomposition of Symmetric Nonlinear Control Systems
对称非线性控制系统的串级解耦标准形

It is shown that a nonlinear control system possessing symmetries has locally a normal form with cascade decomposition. This normal form consists of two subsystems. One is a independent subsystem of the dimension equal to the difference of the dimensions between the total system and the symmetry Lie group. The other is a subsystem without controls. Using differential geometric method and choosing properly a few symmetric functions of coordinate transformation whose Lie derivatives with respect to input vector fields all vanish, we can construct the normal form.