### Abstract

This paper considers the problem of designing near-optimal finite-dimensional controllers for stable multiple-input multiple-output (MIMO) distributed parameter plants under sampled-data control. A weighted H
^{∞}-style mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a `natural' finite-dimensional sampled-data optimization. A priori computable conditions are given on the approximants such that the resulting finite-dimensional controllers stabilize the sampled-data controlled distributed parameter plant and are near-optima. The proof relies on the fact that the control input is appropriately penalized in the optimization. This technique also assumes and exploits the fact that the plant can be approximated uniformly by finite-dimensional systems. Moreover, it is shown how the optimal performance may be estimated to any desired degree of accuracy by solving a single finite-dimensional problem using a suitable finite-dimensional approximant. The constructions given are simple. Finally, it should be noted that no infinite-dimensional spectral factorizations are required. In short, the paper provides a straight forward control design approach for a large class of MIMO distributed parameter systems under sampled-data control.

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

Publisher | IEEE |

Pages | 521-526 |

Number of pages | 6 |

Volume | 1 |

State | Published - 1997 |

Event | Proceedings of the 1997 36th IEEE Conference on Decision and Control. Part 1 (of 5) - San Diego, CA, USA Duration: Dec 10 1997 → Dec 12 1997 |

### Other

Other | Proceedings of the 1997 36th IEEE Conference on Decision and Control. Part 1 (of 5) |
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City | San Diego, CA, USA |

Period | 12/10/97 → 12/12/97 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

^{∞}mixed-sensitivity minimization for stable distributed parameter plants under sampled-data control In

*Proceedings of the IEEE Conference on Decision and Control*(Vol. 1, pp. 521-526). IEEE.

**Weighted H
^{∞} mixed-sensitivity minimization for stable distributed parameter plants under sampled-data control
.** / Carter, Delano R.; Rodriguez, Armando.

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

^{∞}mixed-sensitivity minimization for stable distributed parameter plants under sampled-data control in

*Proceedings of the IEEE Conference on Decision and Control.*vol. 1, IEEE, pp. 521-526, Proceedings of the 1997 36th IEEE Conference on Decision and Control. Part 1 (of 5), San Diego, CA, USA, 12/10/97.

^{∞}mixed-sensitivity minimization for stable distributed parameter plants under sampled-data control In Proceedings of the IEEE Conference on Decision and Control. Vol. 1. IEEE. 1997. p. 521-526

}

TY - GEN

T1 - Weighted H ∞ mixed-sensitivity minimization for stable distributed parameter plants under sampled-data control

AU - Carter, Delano R.

AU - Rodriguez, Armando

PY - 1997

Y1 - 1997

N2 - This paper considers the problem of designing near-optimal finite-dimensional controllers for stable multiple-input multiple-output (MIMO) distributed parameter plants under sampled-data control. A weighted H ∞-style mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a `natural' finite-dimensional sampled-data optimization. A priori computable conditions are given on the approximants such that the resulting finite-dimensional controllers stabilize the sampled-data controlled distributed parameter plant and are near-optima. The proof relies on the fact that the control input is appropriately penalized in the optimization. This technique also assumes and exploits the fact that the plant can be approximated uniformly by finite-dimensional systems. Moreover, it is shown how the optimal performance may be estimated to any desired degree of accuracy by solving a single finite-dimensional problem using a suitable finite-dimensional approximant. The constructions given are simple. Finally, it should be noted that no infinite-dimensional spectral factorizations are required. In short, the paper provides a straight forward control design approach for a large class of MIMO distributed parameter systems under sampled-data control.

AB - This paper considers the problem of designing near-optimal finite-dimensional controllers for stable multiple-input multiple-output (MIMO) distributed parameter plants under sampled-data control. A weighted H ∞-style mixed-sensitivity measure which penalizes the control is used to define the notion of optimality. Controllers are generated by solving a `natural' finite-dimensional sampled-data optimization. A priori computable conditions are given on the approximants such that the resulting finite-dimensional controllers stabilize the sampled-data controlled distributed parameter plant and are near-optima. The proof relies on the fact that the control input is appropriately penalized in the optimization. This technique also assumes and exploits the fact that the plant can be approximated uniformly by finite-dimensional systems. Moreover, it is shown how the optimal performance may be estimated to any desired degree of accuracy by solving a single finite-dimensional problem using a suitable finite-dimensional approximant. The constructions given are simple. Finally, it should be noted that no infinite-dimensional spectral factorizations are required. In short, the paper provides a straight forward control design approach for a large class of MIMO distributed parameter systems under sampled-data control.

UR - http://www.scopus.com/inward/record.url?scp=0031369562&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031369562&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0031369562

VL - 1

SP - 521

EP - 526

BT - Proceedings of the IEEE Conference on Decision and Control

PB - IEEE

ER -