Feedback equivalence and decomposition of nonlinear control systems

The feedback equivalence problems of nonlinear control systems are studied by introducing the notion of virtual decomposition. It is shown that the feedback equivalence problem is reduced to the feedback equivalence problems of decomposed virtual subsystems. A sufficient condition for two general nonlinear control systems being feedback equivalent is derived. This result is applied to the linearization problem, and a necessary and sufficient condition is derived. By applying the theorem which gives the relationship between the decomposed structure and the vector fields of the system, the linearizability condition derived is shown to be another expression of the known linearizability condition