A separation principle for a class of euler-lagrange systems

We have addressed in this chapter, the problem of output feedback trajectory tracking of Euler Lagrange systems. For a subclass of these systems (including manipulators), characterised by certain factorisation, we have provided a separation principle. Our main result establishes that, if a globally exponentially stabilising state feedback controller can be implemented using the state estimates provided by a globally exponentially convergent observer; the overall closed loop system, remains uniformly globally asymptotically stable. Even though our results cannot be directly applied to robot manipulators, for these systems, we have conjectured the weaker property of UGS plus global uniform convergence of part of the state variables. These include the position and velocity tracking errors. The proof of the latter is currently under investigation.

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