Robust Feedback Linearization using Extended High-Gain Observers

We consider a partially feedback linearizable system with stable zero dynamics. The system is uncertain and only the output is measured. Consequently, exact feedback linearization is not applicable. We propose to design an extended high-gain observer to recover unmeasured derivatives of the output and an extra one, which contains information about the uncertainty. The observer can be stabilized via feedback linearization followed by a linear control design, such as pole placement or LQR. After a short peaking period, a partial state vector, which includes the output and its derivatives, will be in a small neighborhood of the state of the observer; therefore, the performance achievable under exact feedback linearization will be recovered