Robust output regulation with nonlinear exosystems

For over a decade, the solvability of the nonlinear robust output regulation problem relies on the assumption that the exosystem is linear and neurally stable. Thus the only exogenous signal that can be accommodated by the existing theory is a combination of finitely many step functions and sinusoidal functions. We will show that it is possible to find controllers that can admit exogenous signals produced by nonlinear exosystems. An example with the well known Van der Pol oscillator as the exosystem is given to illustrate our approach.