On passivity‐based output feedback global stabilization of euler‐lagrange systems

Abstract

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 suitable damping is present in the system. These properties motivated the development of a passivity‐based controller design methodology which aims at modifying the potential energy of the closed loop and the addition of the required dissipation. To achieve the latter objective measurement of the generalized velocities is typically required. Our main contribution in this paper is the proof that damping injection without velocity measurement is possible via the inclusion of a dynamic extension provided the system satisfies a dissipation propggation condition. This allows us to determine a class of Euler‐Lagrange systems that can be globally asymptotically stabilized with dynamic output feedback. We illustrate this result with the problem of set‐point control of elastic joints robots. Our research contributes, if modestly, to the development of a theory for stabilization of nonlinear systems with physical structures which effectively exploits its energy dissipation properties.