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In this book, we derive a sufficient condition for asymptotic stability of the zero solution of delay-difference system of Hopfield neural networks and cellular neural networks in the terms of certain matrix inequalities by using the second Lyapunov method. The result has been applied to obtain new stability conditions for some classes of delay-difference equation such as delay-difference system of Hopfield neural networks with multiple delays, delay-difference control system of Hopfield neural networks, delay-difference control system of Hopfield neural networks with multiple delays, delay-difference system of Hopfield neural networks with time-varying delay, delay-difference system of Hopfield neural networks with multiple time-varying delays, delay-difference system of cellular neural networks with multiple delays, delay-difference control system of cellular neural networks, delay-difference control system of cellular neural networks with multiple delays, delay-difference system of cellular neural networks with time-varying delay and delay-difference system of cellular neural networks with multiple time-varying delays in the terms of certain matrix inequalities.