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${H}_{\infty }$ filtering of networked discrete-time systems with random packet losses. (English) Zbl 1187.93132
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:
 93E11 Filtering in stochastic control 93C55 Discrete-time control systems 90B18 Communication networks (optimization) 60J05 Discrete-time Markov processes on general state spaces 90C25 Convex programming