## 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) |
---|---|

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 |
---|---|

Country/Territory | 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

## Fingerprint

Dive into the research topics of 'H^{∞}mixed sensitivity minimization for stable infinite-dimensional plants subject to convex constraints'. Together they form a unique fingerprint.