Event-triggered network-based ℓ1-gain filtering for positive linear systems

ABSTRACT The ℓ1-gain filtering problem of positive linear discrete-time systems based on networked communication is investigated in this paper. A filter system model in which the sampled signals are transmitted through the unreliable communication channels is constructed for a positive system. An event-triggered scheme in a linear form, which is different from the prior literatures, is designed to determine whether the signal packet should be transmitted to the filter or not. Network-induced delays are considered while handling the packet transmission. By using the linear Lyapunov function method, a sufficient condition to ensure the existence of the network-based positive filter satisfying ℓ1-gain performance is proposed. The desired filter design method for the positive system is presented by using a linear programming approach. A numerical example with practical considerations is given to verify the proposed theoretical results.

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