## Abstract

This paper addresses the common engineering practice of specifying a required probability of attaining some performance level. The problem setup is that of a standard robust H_{∞} performance analysis of a parameter-dependent system, except that the parameter hyper-rectangle (box) shrinks in the analysis in order to accommodate a polytopic performance goal that is better than the one attainable for the original parameter box. An affine-quadratic, multiconvex approach is applied to reduce the overdesign that is inherent in the quadratic approach. A version of the Bounded Real Lemma (BRL) in the form of BiLinear Matrix Inequalities (BLMIs) guarantees a minimum H_{∞}-norm for a prescribed probability. These BLMIs are solved using an iterative algorithm. A uniform distribution is assumed for the system parameters, according to the uniformity principle. The probability requirement is expressed by a set of LMIs that is derived by extending an existing second-order cone method; these LMIs are to be concurrently solved with the BRL BLMIs. The proposed analysis is demonstrated via a 2-parameter example.

Original language | English |
---|---|

Title of host publication | IFAC Proceedings Volumes (IFAC-PapersOnline) |

Editors | Gabriel Ferrate, Eduardo F. Camacho, Luis Basanez, Juan. A. de la Puente |

Publisher | IFAC Secretariat |

Pages | 175-180 |

Number of pages | 6 |

Edition | 1 |

ISBN (Print) | 9783902661746 |

DOIs | |

State | Published - 2002 |

Event | 15th World Congress of the International Federation of Automatic Control, 2002 - Barcelona, Spain Duration: 21 Jul 2002 → 26 Jul 2002 |

### Publication series

Name | IFAC Proceedings Volumes (IFAC-PapersOnline) |
---|---|

Number | 1 |

Volume | 35 |

ISSN (Print) | 1474-6670 |

### Conference

Conference | 15th World Congress of the International Federation of Automatic Control, 2002 |
---|---|

Country/Territory | Spain |

City | Barcelona |

Period | 21/07/02 → 26/07/02 |

## Keywords

- Affine quadratic stability
- H-infinity optimization
- Probabilistic performance analysis
- Robustness

## Fingerprint

Dive into the research topics of 'Probability-guaranteed robust H_{∞}performance analysis'. Together they form a unique fingerprint.