I am working on stability of nonlinear switched systems and recently, I have proven that switched systems with homogeneous, cooperative, Irreducible and commuting vector fields , i.e., vector fields with Lie bracket equal to 0, are D-stable under some condition. I was trying to find an example for such systems but surprisingly, I could not find any in the papers which have dealt with them.
Does anybody know a good example of commuting nonlinear vector fields? And are there any significance to such systems (from physical point of view)?



Commuting Nonlinear Vector Fields
Any set of nonlinear co-ordinates gives you a corresponding set of commuting vector fields. So any of the co-ordinates listed in the "See also" section of 


<http://en.wikipedia.org/wiki/Elliptic_coordinates>


gives an example.


