Remarks on the robust output regulation problem for nonlinear systems

The robust nonlinear output regulation problem was first solved under a polynomial condition on an input feedforward function. Another condition was given later which appears less restrictive than the first one. In this note, we will show that both these two conditions lead to the same sufficient condition that the input feedforward function along the trajectories of the exosystem is a sum of finitely many harmonics, or what is called trigonometric polynomial