### Abstract

This paper considers the problem of designing near-optimal finite-dimensional compensators for unstable infinite-dimensional plants. Standard weighted H^{∞} sensitivity measures are used to define the notion of optimality. The method of solution is based on finite-dimensional techniques applied to finite-dimensional approximants of the original plant. The difficulties which arise from such an approach can be attributed to two factors. First, there is the lack of continuity of the performance measures with respect to perturbations in the plant, even with the graph topology. Second, there are many infinite-dimensional plants which cannot be approximated uniformly in the graph topology. It is shown in this paper, for the sensitivity minimization problem, that it is sufficient to obtain approximants of the plant on compact sets, provided that the inner part of the plant's `numerator coprime factor' is approximated in some sense. Constructive algorithms are presented. New results on the convergence of actual closed loop transfer functions are also given.

Original language | English (US) |
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Title of host publication | American Control Conference |

Publisher | Publ by IEEE |

Pages | 2155-2159 |

Number of pages | 5 |

ISBN (Print) | 0780308611 |

State | Published - Jan 1 1993 |

Event | Proceedings of the 1993 American Control Conference - San Francisco, CA, USA Duration: Jun 2 1993 → Jun 4 1993 |

### Publication series

Name | American Control Conference |
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### Other

Other | Proceedings of the 1993 American Control Conference |
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City | San Francisco, CA, USA |

Period | 6/2/93 → 6/4/93 |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

^{∞}sensitivity minimization for unstable infinite-dimensional plants. In

*American Control Conference*(pp. 2155-2159). (American Control Conference). Publ by IEEE.