### Abstract

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 language | English |
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Title of host publication | IFAC Proceedings Volumes (IFAC-PapersOnline) |

Editors | Gabriel Ferrate, Eduardo F. Camacho, Luis Basanez, Juan. A. de la Puente |

Publisher | IFAC Secretariat |

Pages | 109-114 |

Number of pages | 6 |

Edition | 1 |

ISBN (Print) | 9783902661746 |

DOIs | |

Publication status | Published - 2002 |

Event | 15th World Congress of the International Federation of Automatic Control, 2002 - Barcelona, Spain Duration: Jul 21 2002 → Jul 26 2002 |

### Publication series

Name | IFAC Proceedings Volumes (IFAC-PapersOnline) |
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Number | 1 |

Volume | 35 |

ISSN (Print) | 1474-6670 |

### Other

Other | 15th World Congress of the International Federation of Automatic Control, 2002 |
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Country | Spain |

City | Barcelona |

Period | 7/21/02 → 7/26/02 |

### Keywords

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

### ASJC Scopus subject areas

- Control and Systems Engineering

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## Cite this

*IFAC Proceedings Volumes (IFAC-PapersOnline)*(1 ed., pp. 109-114). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 35, No. 1). IFAC Secretariat. https://doi.org/10.3182/20020721-6-es-1901.00268