Input-output linearisation of nonlinear systems with ill-defined relative degree: the ball & beam revisited

D.J. Leith, W.E. Leithead

Research output: Contribution to conferencePaperpeer-review

11 Citations (Scopus)


In this note it is established that for SISO systems lack of welldefined relative degree is not an obstacle to exact inversion. Sufficient conditions for the existence of exact linearising inputs are established. Exact tracking solutions of a number of example systems, including the ball and beam system studied by Hauser and others, are analysed. It is shown that linearising inputs may be (i) highly non-unique, (ii) discontinuous and include impulses etc., (iii) fragile. A framework is established for approximate linearisation whereby exact linearising inputs are formulated as the limits of sequences of realisable,arbitrarily accurate linearising inputs. This framework is constructive in nature and of key importance when the exact linearising inputs are, for example, unrealisable.
Original languageEnglish
Number of pages5
Publication statusPublished - 27 Jun 2001
EventAmerican Control Conference - Arlington, VA, USA
Duration: 25 Jun 200127 Jun 2001


ConferenceAmerican Control Conference
CityArlington, VA, USA


  • input-output linearisation
  • nonlinear systems
  • ill-defined
  • ball & beam
  • revisited

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