### 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 |

Place of Publication | Piscataway, NJ, United States |

Publisher | Publ by IEEE |

Pages | 2155-2159 |

Number of pages | 5 |

ISBN (Print) | 0780308611 |

State | Published - 1993 |

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

### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

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

*American Control Conference*(pp. 2155-2159). Piscataway, NJ, United States: Publ by IEEE.

**H ^{∞} sensitivity minimization for unstable infinite-dimensional plants.** / Rodriguez, Armando; Cloutier, James R.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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

*American Control Conference.*Publ by IEEE, Piscataway, NJ, United States, pp. 2155-2159, Proceedings of the 1993 American Control Conference, San Francisco, CA, USA, 6/2/93.

^{∞}sensitivity minimization for unstable infinite-dimensional plants. In American Control Conference. Piscataway, NJ, United States: Publ by IEEE. 1993. p. 2155-2159

}

TY - GEN

T1 - H∞ sensitivity minimization for unstable infinite-dimensional plants

AU - Rodriguez, Armando

AU - Cloutier, James R.

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0027335283&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027335283&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0027335283

SN - 0780308611

SP - 2155

EP - 2159

BT - American Control Conference

PB - Publ by IEEE

CY - Piscataway, NJ, United States

ER -