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**Robust \(H_{\infty}\) filtering for uncertain impulsive stochastic systems under sampled measurements.**
*(English)*
Zbl 1012.93063

This paper is concerned with the problem of robust \(H_{\infty}\) filtering for uncertain impulsive stochastic systems under sampled measurements. The parameter uncertainties are assumed to be time-varying norm-bounded. The aim is to design a stochastically stable filter, using the locally sampled measurements, which ensures both the robust stochastic stability and a prescribed level of \(H_{\infty}\) performance for the filtering error dynamics for all admissible uncertainties. A sufficient condition for the existence of such a filter is proposed in terms of certain linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired filter is given. An example is provided to demonstrate the effectiveness of the proposed approach.

Reviewer: S.K.Ntouyas (Ioannina)

### MSC:

93E11 | Filtering in stochastic control theory |

93B36 | \(H^\infty\)-control |

93C57 | Sampled-data control/observation systems |

93E15 | Stochastic stability in control theory |

93D09 | Robust stability |

34A37 | Ordinary differential equations with impulses |

### Keywords:

\(H_{\infty}\) filtering; impulsive systems; linear matrix inequality; robust filtering; sampled measurements; stable filter; robust stochastic stability
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\textit{S. Xu} and \textit{T. Chen}, Automatica 39, No. 3, 509--516 (2003; Zbl 1012.93063)

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