## Abstract

The problem of finite-horizon H_{∞} tracking for linear time-varying systems with stochastic parameter uncertainties is investigated. We consider three tracking patterns depending on the nature of the reference signal i.e : whether it is perfectly known in advance, measured on line or previewed in a fixed time-interval ahead. The stochastic uncertainties appear in both the dynamic and measurement matrices of the system. For each of the above three cases a game theory approach is applied where, given a specific reference signal, the controller plays against nature which chooses the initial condition and the energy-bounded disturbance. The problems are solved using an expected value of the standard performance index over the stochastic parameters, where necessary and sufficient conditions are found for the existence of a saddle-point equilibrium. The infinite-horizon time-invariant tracking problem is also solved. The theory developed is demonstrated by a simple example.

Original language | English |
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Title of host publication | 2001 European Control Conference, ECC 2001 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 3475-3480 |

Number of pages | 6 |

ISBN (Electronic) | 9783952417362 |

State | Published - 2001 |

Event | 6th European Control Conference, ECC 2001 - Porto, Portugal Duration: 4 Sep 2001 → 7 Sep 2001 |

### Publication series

Name | 2001 European Control Conference, ECC 2001 |
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### Conference

Conference | 6th European Control Conference, ECC 2001 |
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Country/Territory | Portugal |

City | Porto |

Period | 4/09/01 → 7/09/01 |

## Keywords

- LMI
- Stochastic H
- preview tracking
- stochastic uncertainty
- tracking

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