### Abstract

This paper considers the problem of designing near-optimal finite-dimensional sampled-data controllers for single-input single-output (SISO) and possibly unstable distributed parameter plants. 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. Conditions are given on the approximants such that the resulting finite-dimensional controllers stabilize the sampled-data controlled distributed parameter plant and are near-optimal. 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 coprime factors 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 proofs and construction 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 SISO and possibly unstable 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 |

Pages | 313-318 |

Number of pages | 6 |

Volume | 1 |

State | Published - 1998 |

Event | Proceedings of the 1998 37th IEEE Conference on Decision and Control (CDC) - Tampa, FL, USA Duration: Dec 16 1998 → Dec 18 1998 |

### Other

Other | Proceedings of the 1998 37th IEEE Conference on Decision and Control (CDC) |
---|---|

City | Tampa, FL, USA |

Period | 12/16/98 → 12/18/98 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

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

*Proceedings of the IEEE Conference on Decision and Control*(Vol. 1, pp. 313-318)

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

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

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

*Proceedings of the IEEE Conference on Decision and Control.*vol. 1, pp. 313-318, Proceedings of the 1998 37th IEEE Conference on Decision and Control (CDC), Tampa, FL, USA, 12/16/98.

^{∞}mixed-sensitivity minimization for distributed parameter plants under sampled-data control In Proceedings of the IEEE Conference on Decision and Control. Vol. 1. 1998. p. 313-318

}

TY - CHAP

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

AU - Carter, Delano R.

AU - Rodriguez, Armando

PY - 1998

Y1 - 1998

N2 - This paper considers the problem of designing near-optimal finite-dimensional sampled-data controllers for single-input single-output (SISO) and possibly unstable distributed parameter plants. 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. Conditions are given on the approximants such that the resulting finite-dimensional controllers stabilize the sampled-data controlled distributed parameter plant and are near-optimal. 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 coprime factors 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 proofs and construction 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 SISO and possibly unstable distributed parameter systems under sampled-data control.

AB - This paper considers the problem of designing near-optimal finite-dimensional sampled-data controllers for single-input single-output (SISO) and possibly unstable distributed parameter plants. 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. Conditions are given on the approximants such that the resulting finite-dimensional controllers stabilize the sampled-data controlled distributed parameter plant and are near-optimal. 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 coprime factors 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 proofs and construction 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 SISO and possibly unstable distributed parameter systems under sampled-data control.

UR - http://www.scopus.com/inward/record.url?scp=0032255637&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032255637&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:0032255637

VL - 1

SP - 313

EP - 318

BT - Proceedings of the IEEE Conference on Decision and Control

ER -