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(The Sufficient Condition for Stability of Discrete-time Control System of Hopfield Neural
Networks via Matrix Inequalities and Applications)
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Kreangkri Ratchagit1*
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Abstract
In this paper, we derive a sufficient condition for asymptotic stability of the zero solution of delay-
difference control system of Hopfield neural networks in terms of certain matrix inequalities by using a discrete
version of the Lyapunov second method. The result is applied to obtain new asymptotic stability condition for
some class of delay-difference control system such as delay-difference control system of Hopfield neural networks
with multiple delays in terms of certain matrix inequalities. Our results can be well suited for computational
purposes.
Keywords: Asymptotic stability, Hopfield neural networks, Lyapunov function, Delay-difference control system,
Matrix inequalities.
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1°µ‹µ¦¥r —¦.Á„¦¸ ¥ŠÅ„¦ ¦µ„·‹ £µ‡ª·µ‡–·˜«µ˜¦r ‡–³ª·š¥µ«µ˜¦r ¤®µª·š¥µ¨´¥Â¤nËo Á¸¥ŠÄ®¤n 50290
Dr. Kreangkri Ratchagit Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, 50290
*Corresponding author: Ú¦«´¡šr 083-7150524 E-mail:kreangkri@mju.ac.th