## Abstract

Linear discrete-time systems with stochastic uncertainties in their state-space matrices are considered. The problems of finite-horizon state-feedback control and filtering are solved, taking into account possible cross-correlations between the uncertain parameters. In both problems, a cost function is defined which is the expected value of the standard H_{∞} performance index with respect to the uncertain parameters. In the state-feedback case, we derive a necessary and sufficient condition for the cost to be non-positive, for all possible energy bounded exogenous signals. A solution to the filtering problem is obtained by applying the adjoint system. It guarantees a prescribed estimation level of accuracy while minimizing an upper-bound on the covariance of the estimation error. The filtering problem is also analyzed in the stationary case. The results for the state-feedback and the filtering problems are then used to solve the corresponding output-feedback problem. An example is given which demonstrates the use of the theory developed.

Original language | English |
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Title of host publication | European Control Conference, ECC 1999 - Conference Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1310-1315 |

Number of pages | 6 |

ISBN (Electronic) | 9783952417355 |

State | Published - 24 Mar 2015 |

Event | 1999 European Control Conference, ECC 1999 - Karlsruhe, Germany Duration: 31 Aug 1999 → 3 Sep 1999 |

### Publication series

Name | European Control Conference, ECC 1999 - Conference Proceedings |
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### Conference

Conference | 1999 European Control Conference, ECC 1999 |
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Country/Territory | Germany |

City | Karlsruhe |

Period | 31/08/99 → 3/09/99 |

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