On complex non-linear systems with symmetries: controllability preserving decomposition

In this paper, the problems of isomorphic decomposition and controllability of a class of nonlinear systems possessing symmetries, on the basis of quotient systems, is studied. The isomorphic decomposition formations of these systems are derived. Finally, it is shown that controllability of the original systems can be determined by that of the subsystems, which are obtained through isomorphic decomposition. The corresponding sufficient and necessary conditions are given. Two new theoretical results have been proved.