Global asymptotical stability analysis for a kind of discrete-time recurrent neural network with discontinuous activation functions

This paper discusses a kind of discrete-time recurrent neural network with discontinuous activation functions. The theory of difference inclusion is introduced to model discrete-time neural network with discontinuous activation functions. By redefining the equilibrium point of discrete-time recurrent neural network with discontinuous activation functions and then using induction principle, sufficient conditions are derived to ensure global asymptotical stability of the equilibrium points of such neural network. Three examples are presented to verify the validity of our results.