ℓ₁-gain filter design of discrete-time positive neural networks with mixed delays

This paper mainly focuses on the filter design with ℓ₁-gain disturbance attenuation performance for a class of discrete-time positive neural networks. Discrete and distributed time-varying delays occurring in neuron transmission are taken into account. Especially, the probabilistic distribution of distributed delays is described by a Bernoulli random process in the system model. First, criteria on the positiveness and the unique equilibrium of discrete-time neural networks are presented. Second, through linear Lyapunov method, sufficient conditions for globally asymptotic stability with ℓ₁-gain disturbance attenuation performance of positive neural networks are proposed. Third, using the results obtained above, criteria on ℓ₁-gain stability of the established filtering error system are presented, based on which a linear programming (LP) approach is put forward to design the desired positive filter. Finally, two examples of applications to water distribution network and genetic regulatory network are given to demonstrate the effectiveness and applicability of the derived results.