## Abstract

We examine an H^{∞} mixed sensitivity design problem in order to gain an understanding of the pole-zero cancellation phenomenon that is known to occur with such designs. It is shown how the pole-zero cancellation phenomenon is dependent upon the choice of weighting functions used in the problem formulation, and a particular construction of weighting function is given that gives the designer freedom to exploit or prevent the phenomenon. Furthermore, this weighting function is then a mechanism for (partial) pole placement. As a consequence of the construction of this weighting function, it is shown that for a certain class of plant, the Normalized Coprime Factor design procedure of Glover and McFarlane (1989, Robust Controller Design Using Normalized Coprime Factor Plant Descriptions. Springer-Verlag, Berlin) gives rise to (possibly undesirable) pole-zero cancellations. The results are presented for multivariable systems, and are illustrated with a simple design example.

Original language | English |
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Pages (from-to) | 519-530 |

Number of pages | 12 |

Journal | Automatica |

Volume | 28 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1992 May |

## All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Electrical and Electronic Engineering