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Robust ${H}_{\infty }$ finite-horizon filtering with randomly occurred nonlinearities and quantization effects. (English) Zbl 1218.93103
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:
 93E11 Filtering in stochastic control 93E03 General theory of stochastic systems 93C55 Discrete-time control systems 93B36 ${H}^{\infty }$-control