On output feedback stabilization of Euler-Lagrange systems with nondissipative forces

Abstract

This paper provides a solution to the problem of output feedback stabilization of systems described by Euler-Lagrange equations perturbed by nondissipative forces. This class of forces appears in some applications where we must take into account the interaction of the system with its environment. The nonlinear dependence on the unmeasurable part of the state and the loss of the fundamental passivity property render most of the existing results on stabilization of nonlinear systems unapplicable to this problem. The technique we use consists of finding a dynamic output feedback controller and a nonlinear change of coordinates such that the closed loop can be decomposed as a cascade of an asymptotically stable system and an input-to-state stable system. This should be contrasted with the well-known passivity-based technique that aims at a feedback interconnection of passive systems. We believe this design methodology to be of potential applicability to other stabilization problems where passivity arguments are unapplicable.