On global exponential stability of standard and full‐range CNNs
Copyright policy ) Di Marco, Mauro; Forti, Mauro; Grazzini, Massimo; Pancioni, Luca;
On global exponential stability of standard and full‐range CNNs
AbstractThis paper compares the dynamical behaviour of the standard (S) cellular neural networks (CNNs) and the full‐range (FR) CNNs, when the two CNN models are characterized by the same set of parameters (interconnections and inputs). The FR‐CNNs are assumed to be characterized by ideal hard‐limiter nonlinearities with two vertical segments in the i–v characteristic. The main result is that some basic conditions ensuring global exponential stability (GES) of the unique equilibrium point of S‐CNNs, with or without delay, continue to ensure the same property for FR‐CNNs for the same set of parameters. The significance of this result is discussed with respect to the results in a paper by Corinto and Gilli addressing the similarity of the qualitative behaviour of S‐CNNs and FR‐CNNs. FR‐CNNs are analysed in this paper from a rigorous mathematical viewpoint by means of theoretical tools from set‐valued analysis and differential inclusions. In particular, GES is investigated via an extended Lyapunov approach that is applicable to the differential inclusion describing the dynamics of FR‐CNNs. Copyright © 2007 John Wiley & Sons, Ltd.
Italy
- University of Siena Italy
Cellular neural network, Signal theory (characterization, reconstruction, filtering, etc.), Differential inclusion, Lyapunov method, Cellular neural networks; Differential inclusions; Global stability; Lyapunov method, Global stability, Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory, Neural networks for/in biological studies, artificial life and related topics, Global stability of solutions to ordinary differential equations, global stability, 510, differential inclusions, cellular neural networks
Cellular neural network, Signal theory (characterization, reconstruction, filtering, etc.), Differential inclusion, Lyapunov method, Cellular neural networks; Differential inclusions; Global stability; Lyapunov method, Global stability, Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory, Neural networks for/in biological studies, artificial life and related topics, Global stability of solutions to ordinary differential equations, global stability, 510, differential inclusions, cellular neural networks
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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