Asymptotic stability of reference trajectories for nonlinear systems by linear dynamic output feedback

In this contribution we analyze in detail the stability of the linear dynamic output feedback which has been introduced in [1], [2] for the stabilization of trajectories for differentially flat systems and which has been extended to nonflat systems whose linearization about the reference trajectory is controllable [3], [4]. The linearized tracking error dynamics of the closed loop system are shown to be exponentially stable and thus the reference trajectory for the nonlinear system is asymptotically stable. In this contribution also the states of an implementation of the dynamic output feedback are considered and the relations with the state space approach are clarified.