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

• A network-based system is considered in this paper.
• The network-induced delays are modeled by a Markov chain with partly uncertain transition probabilities.
• A reduced-order energy-to-peak filter is designed.
• A numerical example illustrates the effectiveness of the proposed filtering approach.

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 Finsler׳s 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.