Feedback Decoupling for Affine Nonllnear Systems Possesslng Symmetries

Systems possessing symmetries always have good structure They may also have other good properties. In this paper, Feedback decoupling problems for affine nonlinear systems with symmetries are discussed by using the techniques of differential geometry. The concept of derived distributions is firstly defined for systems with symmetries under the actions of compact connected Lie groups. Necessary and sufficient conditions for the solvability of our problem are given. We can see from the results that our conditions are simpler than those of systems without symmetries. This indicates that systems with symmetries always have good structure as well as other good properties indeed.