On mode-dependent H∞H∞ filtering for network-based discrete-time systems

This paper is devoted to the H∞H∞ filtering problem for network-based discrete-time systems subject to network communication constraints. The objective is to design a network-based full-order or reduced-order filter, such that the resulting filtering error system is mean-square stable, while a prescribed H∞H∞ disturbance attenuation levels is satisfied. A Markov chain is used to describe the network-induced delays. Then, a mode-dependent linear filter is considered, whose parameters are scheduled by the network-induced delays. By converting the partially unknown transition probability matrix to be a known convex description, and using the slack matrix approach, a new less conservative mode-dependent sufficient condition for the existence of the desired filter is derived to guarantee that the filtering error system is stochastically stable while satisfying a given H∞H∞ performance. Based on this condition, the filter design method is proposed, and by solving some convex linear matrix inequalities, the explicit of the desired filer gain matrices is also given. Finally, a practical example is included to illustrate the effectiveness of the proposed method.

► We investigate the filtering problem for network-based systems.
► The network-induced delays are modeled via the Markov chain with partially known transition probabilities.
► The derived results are less conservative than the published ones.