Robust reduced-order l₂-l_∞ filtering for network-based discrete-time linear systems

This paper investigates the l₂-l_∞ filtering problem for a class of discrete-time system subject to network-induced delays. The objective is to design a reduced-order filter, such that the estimation errors converge to zero, while an l₂-l_∞ performance is satisfied. A Markov chain with partly unknown transition probabilities is used to describe the network-induced delay. Then, a delay-dependent linear filter is considered, whose parameters are described by the network-induced delay. By using Finslers lemma, sufficient conditions in terms of linear matrix inequalities (LMIs) for the existence of the desired filter are derived, which guarantee that estimation errors converge to zero with an l₂-l_∞ performance γ. By solving those LMIs, filter gain matrices can be calculated. Finally, numerical simulations are given to illustrate that the designed filter is successful even in the existence of network-induced delays.