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Zbl 1187.93132
Zhang, Wen-An; Yu, Li; Song, Hongbo
$H_\infty$ filtering of networked discrete-time systems with random packet losses.
(English)
[J] Inf. Sci. 179, No. 22, 3944-3955 (2009). ISSN 0020-0255

Summary: This paper studies the $H_\infty$ filtering problem for networked discrete-time systems with random packet losses. The general Multiple-Input-Multiple-Output (MIMO) filtering system is considered. The multiple measurements are transmitted to the remote filter via distinct communication channels, and each measurement loss process is described by a two-state Markov chain. Both the mode-independent and the mode-dependent filters are considered, and the resulting filtering error system is modelled as a discrete-time Markovian system with multiple modes. A necessary and sufficient condition is derived for the filtering error system to be mean-square exponentially stable and achieve a prescribed $H_\infty$ noise attenuation performance. The obtained condition implicitly establishes a relation between the packet loss probability and two parameters, namely, the exponential decay rate of the filtering error system and the $H_\infty$ noise attenuation level. A convex optimization problem is formulated to design the desired filters with minimized $H_\infty$ noise attenuation level bound. Finally, an illustrative example is given to show the effectiveness of the proposed results.
MSC 2000:
*93E11 Filtering in stochastic control
93C55 Discrete-time control systems
90B18 Communication networks
60J05 Markov processes with discrete parameter
90C25 Convex programming

Keywords: $H_\infty$ filtering; packet losses; communication network; Markovian systems; exponential stability

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