H∞ filtering of networked discrete-time systems with random packet losses

This paper studies the H∞ 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∞ 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∞ noise attenuation level. A convex optimization problem is formulated to design the desired filters with minimized H∞ noise attenuation level bound. Finally, an illustrative example is given to show the effectiveness of the proposed results.