## Abstract

In this paper we develop a H_{∞} type theory, from the dissipation point of view, for a large class of time-continuous stochastic nonlinear systems. In particular, we introduce 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. Having discussed certain properties of stochastic dissipative systems, we consider time-varying nonlinear systems for which we establish a connection between what is called the L_{2}-gain property and the solution to a certain Hamilton-Jacobi inequality (HJI), that may be viewed as a bounded real lemma for stochastic nonlinear systems. The time-invariant case with infinite horizon is also considered, where for this case we synthesize a worst case based stabilizing controller. Stability in this case is taken to be in the mean-square sense. In the stationary case, the problem of robust state-feedback control 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 IEEE Conference on Decision and Control |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 5025-5030 |

Number of pages | 6 |

ISBN (Print) | 0780379241 |

DOIs | |

State | Published - 1 Jan 2003 |

Event | 42nd IEEE Conference on Decision and Control - Maui, HI, United States Duration: 9 Dec 2003 → 12 Dec 2003 |

### Publication series

Name | Proceedings of the IEEE Conference on Decision and Control |
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Volume | 5 |

ISSN (Print) | 0743-1546 |

ISSN (Electronic) | 2576-2370 |

### Conference

Conference | 42nd IEEE Conference on Decision and Control |
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Country/Territory | United States |

City | Maui, HI |

Period | 9/12/03 → 12/12/03 |

## ASJC Scopus subject areas

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

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