Delay-dependent and delay-independent passivity of a class of recurrent neural networks with impulse and multi-proportional delays

The problem for passivity of a class of recurrent neural networks (RNNs) with impulse and multi-proportional delays is investigated in this paper. Several delay-dependent and delay-independent passivity criteria for the given system are obtained by establishing appropriate Lyapunov-krasovskill functionals and applying matrix inequality approach. The passivity criteria here are presented in the form of linear matrix inequalities (LMIs), which can be easily verified by Matlab Toolbox. Simultaneously, the criteria obtained here include the passivity results of RNNs without impulse or without delays as special cases and can also be extended to other RNNs with more complicated impulsive noise. Finally, two numerical examples with some simulations shows that the proposed results are effective.