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 1/2. 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.
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|Titolo:||Lojasiewicz inequality and exponential convergence of the full-range model of CNNs|
|Citazione:||DI MARCO, M., Forti, M., Grazzini, M., & Pancioni, L. (2012). Lojasiewicz inequality and exponential convergence of the full-range model of CNNs. INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, 40, 409-419.|
|Appare nelle tipologie:||1.1 Articolo in rivista|