We consider nonlinear affine plants whose measurement output is of dimension larger than the dimension of the external input. General sufficient solvability conditions are given.
Explicit solutions are available in the local and semilocal cases.
The former concerns a certain neighborhood of the origin in the closed loop state-space, while the latter assumes that the trajectories are restricted to a neighborhood of an invariant manifold. The issue of the controller order is addressed and a reduced order controller is obtained in the local case. A new generalization of the chain-scattering formalism provides a very useful framework for solving this problem.