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On global exponential stability of standard and full‐range CNNs

2007; Wiley; Volume: 36; Issue: 5-6 Linguagem: Inglês

10.1002/cta.451

1097-007X

Mauro Di Marco, Mauro Forti, Massimo Grazzini, Luca Pancioni,

Nonlinear Dynamics and Pattern Formation

Abstract This 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.