ON PASSIVITY-BASED OUTPUT-FEEDBACK GLOBAL STABILIZATION OF EULER-LAGRANGE SYSTEMS

It is well known that in systems described by Euler-Lagrange equations the stability of the equilibria is determined by the potential energy function. Further, these equilibria are asymptotically stable if suit able damping is present in the system. These properties motivated the development of a passivity-based controller design methodology which a ims at modifying the potential energy of the closed loop and the addit ion of the required dissipation. To achieve the latter objective measu rement of the generalized velocities is typically required. Our main c ontribution in this paper is the proof that damping injection without velocity measurement is possible via the inclusion of a dynamic extens ion provided the system satisfies a dissipation propagation condition. This allows us to determine a class of Euler-Lagrange systems that ca n be globally asymptotically stabilized with dynamic output feedback. We illustrate this result with the problem of set-point control of ela stic joints robots. Our research contributes, if modestly, to the deve lopment of a theory for stabilization of nonlinear systems with physic al structures which effectively exploits its energy dissipation proper ties.