Decoupling and disturbance decoupling of a class of homogeneous polynomial systems-A subspace approach

We consider control systems of the type x = f(x) + ??i=1 m biui + ??j k = djwj,x??Rn,f(x) is a homogeneous polynomial vector field, bi, dj are constant vectors and the outputs are linear functions of states. We show that the well known subspace theory for linear systems on decoupling, disturbance decoupling etc. extend in a natural way to this class yielding algorithms which are direct generalizations of the corresponding algorithms in the linear theory. These computations are much more simple than the more general algorithms required in the geometric theory of nonlinear systems as found in [11] for example.