Linear output selection for feedback linearization

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


The problem of selecting a linear scalar output y = Kx for a single-input nonlinear dynamic system given in input-affine form (x = f(x) + g(x)u) is considered in this paper. In the general case, when the zero dynamics is hard to investigate analytically, K is suggested to be the resulting feedback gain of an LQ linear optimal control problem for the linearized model. The advantageous properties of the LQ design (gain and phase margins, etc.) known for linear systems enable to obtain an at least locally asymptotically stable, yet simple nonlinear controller if the linear output y = Kx is used for feedback linearization. With this output selection, the relative degree of the open loop system can be easily set to 1 at the desired operating point and it possesses locally (or globally) asymptotically stable zero dynamics. It is shown on examples that the resulting closed loop nonlinear system can be stable in a wide neighborhood of the operating point. The concepts are illustrated on two characteristic nonlinear systems of two different application domain: an inverted pendulum and a continuous fermenter.

Original languageEnglish
Title of host publicationIFAC Proceedings Volumes (IFAC-PapersOnline)
EditorsGabriel Ferrate, Eduardo F. Camacho, Luis Basanez, Juan. A. de la Puente
PublisherIFAC Secretariat
Number of pages6
ISBN (Print)9783902661746
Publication statusPublished - 2002
Event15th World Congress of the International Federation of Automatic Control, 2002 - Barcelona, Spain
Duration: Jul 21 2002Jul 26 2002

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
ISSN (Print)1474-6670


Other15th World Congress of the International Federation of Automatic Control, 2002


  • Feedback linearization
  • Nonlinear systems
  • Output variables
  • Zero dynamics

ASJC Scopus subject areas

  • Control and Systems Engineering

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    Szederkényi, G., Hangos, K. M., Bokor, J., & Vámos, T. (2002). Linear output selection for feedback linearization. In G. Ferrate, E. F. Camacho, L. Basanez, & J. A. de la Puente (Eds.), IFAC Proceedings Volumes (IFAC-PapersOnline) (1 ed., pp. 109-114). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 35, No. 1). IFAC Secretariat.