### Abstract

The problem of designing near-optimal finite-dimensional controllers for stable multiple-input multiple-output (MIMO) distributed parameter plants under multi-rate sampled-data control is discussed in this paper. A weighted ℋ
^{∞}-style mixed-sensitivity measure penalizing the control is used to define the concept of optimality. Controllers are found by solving a finite-dimensional sampled-data optimization. A priori computable conditions for the approximants are provided such that the resulting finite-dimensional controllers stabilize the multi-rate sampled-data controlled distributed parameter plant and are near-optimal. The proof is dependent upon a key fact that the control input is appropriately penalized in the optimization. Another assumption of the presented technique is the plant may be approximated uniformly by finite-dimensional systems. It is shown how the optimal performance may be approximated to any desirable level of accuracy by solving a single finite-dimensional problem using a suitable finite-dimensional approximant. No infinite-dimensional spectral factorizations have been utilized. This paper provides a straight forward approach of control design for a large class of MIMO distributed parameter systems under multi-rate sampled-data control.

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

Pages | 2881-2886 |

Number of pages | 6 |

Volume | 4 |

Publication status | Published - 2003 |

Event | 2003 American Control Conference - Denver, CO, United States Duration: Jun 4 2003 → Jun 6 2003 |

### Other

Other | 2003 American Control Conference |
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Country | United States |

City | Denver, CO |

Period | 6/4/03 → 6/6/03 |

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### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

^{2}Mixed Sensitivity Optimization In

*Proceedings of the American Control Conference*(Vol. 4, pp. 2881-2886)