Controlled invariance for nonlinear systems: Two worked examples

In this note, we present two worked examples of disturbance decoupling for nonlinear systems, using the concept of controlled invariance, which was recently generalized to nonlinear systems. In the first example, we explicitly construct a feedback which decouples a disturbance from the vertical components of the axes of a rotating rigid body, while the second example deals with a particle in a potential field subject to a disturbance.