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$$H_{\infty }$$ filtering with randomly occurring sensor saturations and missing measurements. (English) Zbl 1244.93162
Summary: In this paper, the $$H_{\infty }$$ filtering problem is investigated for a class of nonlinear systems with randomly occurring incomplete information. The considered incomplete information includes both the sensor saturations and the missing measurements. A new phenomenon of sensor saturation, namely, Randomly Occurring Sensor Saturation (ROSS), is put forward in order to better reflect the reality in a networked environment such as sensor networks. A novel sensor model is then established to account for both the ROSS and missing measurement in a unified representation by using two sets of Bernoulli distributed white sequences with known conditional probabilities. Based on this sensor model, a regional $$H_{\infty }$$ filter with a certain ellipsoid constraint is designed such that the filtering error dynamics is locally mean-square asymptotically stable and the $$H_{\infty }$$-norm requirement is satisfied. Note that the regional $$l_{2}$$ gain filtering feature is specifically developed for the random saturation nonlinearity. The characterization of the desired filter gains is derived in terms of the solution to a convex optimization problem that can be easily solved by using the semidefinite program method. Finally, a simulation example is employed to show the effectiveness of the filtering scheme proposed in this paper.

##### MSC:
 93E11 Filtering in stochastic control theory 93B36 $$H^\infty$$-control 93C55 Discrete-time control/observation systems 93C10 Nonlinear systems in control theory 90C22 Semidefinite programming
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