This correspondence is concerned with network-based H ∞ filtering for discrete-time systems. The output signals of the system under consideration are transmitted to the filter through a constraint communication network, which usually leads to network-induced delays and packet dropouts. By introducing a logic data packet processor to choose the newest data signal from the network to actuate the filter, network-induced delays and packet dropouts are modeled as a Markov chain taking values in a finite set. As a result, the filter to be designed is modeled as a Markov jumping linear filter. By introducing some slack matrix variables in terms of probability identity, a less conservative bounded real lemma (BRL) is derived to ensure that the filtering error system is stochastically stable with a prescribed H ∞ level. Based on this BRL, suitable H ∞ filters are designed by employing a cone complementary approach. A practical example on the Leslie model about some certain pest's structured population dynamics is given to show the effectiveness of the proposed approach.