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Zbl 1218.93103
Shen, Bo; Wang, Zidong; Shu, Huisheng; Wei, Guoliang
Robust $H_\infty $ finite-horizon filtering with randomly occurred nonlinearities and quantization effects. (English)
[J] Automatica 46, No. 11, 1743-1751 (2010). ISSN 0005-1098

Summary: In this paper, the robust $H_\infty $ finite-horizon filtering problem is investigated for discrete time-varying stochastic systems with polytopic uncertainties, randomly occurred nonlinearities as well as quantization effects. The randomly occurred nonlinearity, which describes the phenomena of a nonlinear disturbance appearing in a random way, is modeled by a Bernoulli distributed white sequence with a known conditional probability. A new robust $H_\infty $ filtering technique is developed for the addressed Itô-type discrete time-varying stochastic systems. Such a technique relies on the forward solution to a set of recursive linear matrix inequalities and is therefore suitable for on-line computation. It is worth mentioning that, in the filtering process, the information of both the current measurement and the previous state estimate is employed to estimate the current state. Finally, a simulation example is exploited to show the effectiveness of the method proposed in this paper.

MSC 2000:: *93E11 Filtering in stochastic control
93E03 General theory of stochastic systems
93C55 Discrete-time control systems
93B36 $H^\infty$-control

Keywords: stochastic systems; discrete time-varying systems; $H_\infty $ filtering; recursive linear matrix inequalities; randomly occurred nonlinearities; quantization effects

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Zentralblatt MATH Berlin [Germany]