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In this study, the authors consider an H ∞ filtering problem for discrete-time singular systems with lossy measurements. The authors introduce the stochastic variable satisfying Bernoulli random binary distribution to model the measured outputs. This measurement mode can be used to characterise the effect of data-loss in information transmissions across limited bandwidth communication channels over a wide area. The authors design a filter to cope with the losses, which ensures not only the mean-square stochastic stability but also a prescribed H ∞ filtering performance for filtering the error singular system. They also derive sufficient conditions for the existence of such a filter. Finally, the authors give a numerical example to illustrate the effectiveness of the proposed approach.