### Abstract

An approximate/design approach is taken to the problem of designing near-optimal finite-dimensional compensators for scalar infinite dimensional plants. The criteria used to determine optimality are standard H
^{∞} weighted sensitivity and mixed-sensitivity measures. More specifically, it is shown that, given a 'suitable' finite-dimensional approximant for an infinite-dimensional plant, one can solve a 'natural' finite-dimensional problem to obtain a near-optimal finite-dimensional compensator. Moreover, very weak conditions are presented to indicate what a 'suitable' approximant is. In addition, it is shown that the optimal performance can be computed by solving a sequence of finite-dimensional eigenvalue/eigenvector problems rather than the typical infinite-dimensional eigenvalue/eigenfunction problem which appears in the literature.

Original language | English (US) |
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Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Publisher | Publ by IEEE |

Pages | 1814-1820 |

Number of pages | 7 |

Volume | 3 |

State | Published - 1990 |

Event | Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6) - Honolulu, HI, USA Duration: Dec 5 1990 → Dec 7 1990 |

### Other

Other | Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6) |
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City | Honolulu, HI, USA |

Period | 12/5/90 → 12/7/90 |

### Fingerprint

### ASJC Scopus subject areas

- Chemical Health and Safety
- Control and Systems Engineering
- Safety, Risk, Reliability and Quality

### Cite this

^{∞}optimization for stable infinite dimensional systems using finite dimensional techniques In

*Proceedings of the IEEE Conference on Decision and Control*(Vol. 3, pp. 1814-1820). Publ by IEEE.

**Weighted H
^{∞} optimization for stable infinite dimensional systems using finite dimensional techniques
.** / Rodriguez, Armando; Dahleh, Munther A.

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

^{∞}optimization for stable infinite dimensional systems using finite dimensional techniques in

*Proceedings of the IEEE Conference on Decision and Control.*vol. 3, Publ by IEEE, pp. 1814-1820, Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6), Honolulu, HI, USA, 12/5/90.

^{∞}optimization for stable infinite dimensional systems using finite dimensional techniques In Proceedings of the IEEE Conference on Decision and Control. Vol. 3. Publ by IEEE. 1990. p. 1814-1820

}

TY - GEN

T1 - Weighted H ∞ optimization for stable infinite dimensional systems using finite dimensional techniques

AU - Rodriguez, Armando

AU - Dahleh, Munther A.

PY - 1990

Y1 - 1990

N2 - An approximate/design approach is taken to the problem of designing near-optimal finite-dimensional compensators for scalar infinite dimensional plants. The criteria used to determine optimality are standard H ∞ weighted sensitivity and mixed-sensitivity measures. More specifically, it is shown that, given a 'suitable' finite-dimensional approximant for an infinite-dimensional plant, one can solve a 'natural' finite-dimensional problem to obtain a near-optimal finite-dimensional compensator. Moreover, very weak conditions are presented to indicate what a 'suitable' approximant is. In addition, it is shown that the optimal performance can be computed by solving a sequence of finite-dimensional eigenvalue/eigenvector problems rather than the typical infinite-dimensional eigenvalue/eigenfunction problem which appears in the literature.

AB - An approximate/design approach is taken to the problem of designing near-optimal finite-dimensional compensators for scalar infinite dimensional plants. The criteria used to determine optimality are standard H ∞ weighted sensitivity and mixed-sensitivity measures. More specifically, it is shown that, given a 'suitable' finite-dimensional approximant for an infinite-dimensional plant, one can solve a 'natural' finite-dimensional problem to obtain a near-optimal finite-dimensional compensator. Moreover, very weak conditions are presented to indicate what a 'suitable' approximant is. In addition, it is shown that the optimal performance can be computed by solving a sequence of finite-dimensional eigenvalue/eigenvector problems rather than the typical infinite-dimensional eigenvalue/eigenfunction problem which appears in the literature.

UR - http://www.scopus.com/inward/record.url?scp=0025541204&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025541204&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0025541204

VL - 3

SP - 1814

EP - 1820

BT - Proceedings of the IEEE Conference on Decision and Control

PB - Publ by IEEE

ER -