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Distributed $$H_\infty$$-consensus filtering in sensor networks with multiple missing measurements: the finite-horizon case. (English) Zbl 1204.93122
Summary: This paper is concerned with a new distributed $$H_\infty$$-consensus filtering problem over a finite-horizon for sensor networks with multiple missing measurements. The so-called $$H_\infty$$-consensus performance requirement is defined to quantify bounded consensus regarding the filtering errors (agreements) over a finite-horizon. A set of random variables are utilized to model the probabilistic information missing phenomena occurring in the channels from the system to the sensors. A sufficient condition is first established in terms of a set of Difference Linear Matrix Inequalities (DLMIs) under which the expected $$H_\infty$$-consensus performance constraint is guaranteed. Given the measurements and estimates of the system state and its neighbors, the filter parameters are then explicitly parameterized by means of the solutions to a certain set of DLMIs that can be computed recursively. Subsequently, two kinds of robust distributed $$H_\infty$$-consensus filters are designed for the system with norm-bounded uncertainties and polytopic uncertainties. Finally, two numerical simulation examples are used to demonstrate the effectiveness of the proposed distributed filters design scheme.

##### MSC:
 93E11 Filtering in stochastic control theory 93B51 Design techniques (robust design, computer-aided design, etc.)
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