## Abstract

In this paper we develop an H_{∞} filtering theory, from the dissipation point of view, for a large class of time-continuous stochastic nonlinear systems. In particular, we use the notion of stochastic dissipative systems analogously to the familiar notion of dissipation associated with deterministic systems and utilize it as a basis for the development of our theory. We first establish a connection between what is called the L _{2}-gain property and the solution to a certain Hamilton-Jacobi inequalities (HJI), that may be viewed as a bounded real lemma for stochastic nonlinear systems. The infinite time horizon is also considered, where for this case we synthesize a worst case based stable filter which operates on the observation. Stability in this case is taken to be both in the mean-square sense and in probability. The problem of robust filtering is considered in the case of norm-bounded uncertainties. A solution is then derived in terms of linear matrix inequalities.

Original language | English |
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Title of host publication | Proceedings of the 20th IEEE International Symposium on Intelligent Control, ISIC '05 and the 13th Mediterranean Conference on Control and Automation, MED '05 |

Pages | 749-754 |

Number of pages | 6 |

DOIs | |

State | Published - 1 Dec 2005 |

Event | 20th IEEE International Symposium on Intelligent Control, ISIC '05 and the13th Mediterranean Conference on Control and Automation, MED '05 - Limassol, Cyprus Duration: 27 Jun 2005 → 29 Jun 2005 |

### Publication series

Name | Proceedings of the 20th IEEE International Symposium on Intelligent Control, ISIC '05 and the 13th Mediterranean Conference on Control and Automation, MED '05 |
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Volume | 2005 |

### Conference

Conference | 20th IEEE International Symposium on Intelligent Control, ISIC '05 and the13th Mediterranean Conference on Control and Automation, MED '05 |
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Country/Territory | Cyprus |

City | Limassol |

Period | 27/06/05 → 29/06/05 |

## ASJC Scopus subject areas

- Engineering (all)

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