Łojasiewicz inequality and exponential convergence of the full‐range model of CNNs
Mauro Di Marco, Mauro Forti, Massimo Grazzini, Luca Pancioni · International Journal of Circuit Theory and Applications · 2010
SUMMARY This paper considers the Full‐range (FR) model of Cellular Neural Networks (CNNs) in the case where the signal range is delimited by an ideal hard‐limiter nonlinearity with two vertical segments in the i−v characteristic. A Łojasiewicz inequality around any equilibrium point, for a FRCNN with a symmetric interconnection matrix, is proved. It is also shown that the Łojasiewicz exponent is equal to . The main consequence is that any forward solution of a symmetric FRCNN has finite length and is exponentially convergent toward an equilibrium point, even in degenerate situations where the FRCNN possesses non‐isolated equilibrium points. The obtained results are shown to improve the previous results in literature on convergence or almost convergence of symmetric FRCNNs. Copyright © 2010 John Wiley & Sons, Ltd.