## Abstract

The solutions to the optimal l^{2} to l^{2} disturbance rejection problem (H^{∞}) as well as to the LQG (linear quadratic Gaussian) (H^{2}) problem in periodic systems using the lifting technique are presented. Both problems involve a causality condition on the optimal LTI (linear time invariant) compensator when viewed in the lifted domain. The H^{∞} problem is solved using the Nehari's theorem, whereas in the H^{2} problem the solution is obtained using the projection theorem in Hilbert spaces. The authors demonstrate that exactly the same method of solution to the H^{∞} and H^{2} problems in periodic systems applies when considering the same problems in multirate sampled data systems.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the IEEE Conference on Decision and Control |

Publisher | Publ by IEEE |

Pages | 214-216 |

Number of pages | 3 |

ISBN (Print) | 0780304500 |

State | Published - Jan 1992 |

Externally published | Yes |

Event | Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3) - Brighton, Engl Duration: Dec 11 1991 → Dec 13 1991 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
---|---|

ISSN (Print) | 0191-2216 |

### Other

Other | Proceedings of the 30th IEEE Conference on Decision and Control Part 1 (of 3) |
---|---|

City | Brighton, Engl |

Period | 12/11/91 → 12/13/91 |

## ASJC Scopus subject areas

- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization

## Fingerprint

Dive into the research topics of 'H^{∞}and H

^{2}optimal controllers for periodic and multi-rate systems'. Together they form a unique fingerprint.