An additive diagonal-stability condition for absolute exponentialstability of a general class of neural networks
Xue-Bin Liang; Jun Wang
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
Volume 48, Issue 11, Nov 2001 Page(s):1308 - 1317
Digital Object Identifier   10.1109/81.964419
Summary:This paper presents new results on the absolute exponential stability (AEST) of neural networks with a general class of partially Lipschitz continuous and monotone increasing activation functions under a mild condition that the interconnection matrix T of the network system is additively diagonally stable; i.e., for any positive diagonal matrix D₁, there exists a positive diagonal matrix D₂ such that D₂ (T-D₁)+(T-D₁)^TD ₂ is negative definite. This result means that the neural networks with additively diagonally stable interconnection matrices are guaranteed to be globally exponentially stable for any neuron activation functions in the above class, any constant input vectors and any other network parameters. The additively diagonally stable interconnection matrices include diagonally semistable ones and H-matrices with nonpositive diagonal elements as special cases. The obtained AEST result substantially extends the existing ones in the literature on absolute stability (ABST) of neural networks. The additive diagonal stability condition is shown to be necessary and sufficient for AEST of neural networks with two neurons. Summary and discussion of the known results about ABST and AEST of neural networks are also given

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