### Abstract

This paper shows how convex optimization may be used to design near-optimal finite-dimensional compensators for stable linear time invariant (LTI) infinite dimensional plants. The infinite dimensional plant is approximated by a finite dimensional transfer function matrix. The Youla parameterization is used to parameterize the set of all stabilizing LTI controllers and formulate a weighted mixedsensitivity H
^{∞} optimization that is convex in the Youla Q-Parameter. A finite-dimensional (real-rational) stable basis is used to approximate the Q-parameter. By so doing, we transform the associated optimization problem from an infinite dimensional optimization problem involving a search over stable real-rational transfer function matrices in H
^{∞} to a finite-dimensional optimization problem involving a search over a finite-dimensional space. In addition to solving weighted mixed sensitivity H
^{∞} control system design problems, it is shown how subgradient concepts may be used to directly accommodate time-domain specifications (e.g. peak value of control action) in the design process. As such, we provide a systematic design methodology for a large class of infinite-dimensional plant control system design problems. In short, the approach taken permits a designer to address control system design problems for which no direct method exists. Illustrative examples are provided.

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

Pages | 3415-3420 |

Number of pages | 6 |

Volume | 5 |

State | Published - 2005 |

Event | 2005 American Control Conference, ACC - Portland, OR, United States Duration: Jun 8 2005 → Jun 10 2005 |

### Other

Other | 2005 American Control Conference, ACC |
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Country | United States |

City | Portland, OR |

Period | 6/8/05 → 6/10/05 |

### Keywords

- Convex optimization
- H mixed sensitivity
- Infinite dimensional
- Time domain constraints

### ASJC Scopus subject areas

- Control and Systems Engineering

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## Cite this

^{∞}mixed sensitivity minimization for stable infinite-dimensional plants subject to convex constraints In

*Proceedings of the American Control Conference*(Vol. 5, pp. 3415-3420)