Journal
INFORMATION SCIENCES
Volume 179, Issue 19, Pages 3432-3441Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.ins.2009.06.006
Keywords
Neural network; Global asymptotic stability; Neuron activation function; Lyapunov approach; Periodic solution; Differential inclusions
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This paper investigates the global asymptotic stability of the periodic solution for a general class of neural networks whose neuron activation functions are modeled by discontinuous functions with linear growth property. By using Leray-Schauder alternative theorem, the existence of the periodic solution is proved. Based on the matrix theory and generalized Lyapunov approach, a sufficient condition which ensures the global asymptotical stability of a unique periodic solution is presented. The obtained results can be applied to check the global asymptotical stability of discontinuous neural networks with a broad range of activation functions assuming neither boundedness nor monotonicity, and also conform the validity of Forti's conjecture for discontinuous neural networks with linear growth activation functions. Two illustrative examples are given to demonstrate the effectiveness of the present results. (C) 2009 Elsevier Inc. All rights reserved.
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