Physical dissipation and the method of controlled Lagrangians

C. A. Woolsey, A. M. Bloch, N. E. Leonard, J. E. Marsden

Research output: Chapter in Book/Report/Conference proceedingConference contribution

21 Scopus citations


We describe the effect of physical dissipation on stability of equilibria which have been stabilized, in the absence of damping, using the method of controlled Lagrangians. This method applies to a class of underactuated mechanical systems including 'balance' systems such as the pendulum on a cart. Since the method involves modifying a system's kinetic energy metric through feedback, the effect of dissipation is obscured. In particular, it is not generally true that damping makes a feedback-stabilized equilibrium asymptotically stable. Damping in the unactuated directions does tend to enhance stability, however damping in the controlled directions must be 'reversed' through feedback. In this paper, we suggest a choice of feedback dissipation to locally exponentially stabilize a class of controlled Lagrangian systems.

Original languageEnglish (US)
Title of host publication2001 European Control Conference, ECC 2001
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9783952417362
StatePublished - 2001
Externally publishedYes
Event6th European Control Conference, ECC 2001 - Porto, Portugal
Duration: Sep 4 2001Sep 7 2001

Publication series

Name2001 European Control Conference, ECC 2001


Other6th European Control Conference, ECC 2001

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering


  • Dissipative and Energy-based Design
  • Stabilization of Non-linear Systems


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