NDLI: Dynamical Analysis of Full-Range Cellular Neural Networks by Exploiting Differential Variational Inequalities

Content Provider	IEEE Xplore Digital Library
Author	De Sandre, G. Forti, M. Nistri, P. Premoli, A.
Copyright Year	2004
Abstract	The paper considers the full-range (FR) model of cellular neural networks (CNNs) in the case where the neuron nonlinearities are ideal hard-comparator functions with two vertical straight segments. The dynamics of FR-CNNs, which is described by a differential inclusion, is rigorously analyzed by means of theoretical tools from set-valued analysis and differential inclusions. The fundamental property proved in the paper is that FR-CNNs are equivalent to a special class of differential inclusions termed differential variational inequalities. A sound foundation to the dynamics of FR-CNNs is then given by establishing the existence and uniqueness of the solution starting at a given point, and the existence of equilibrium points. Moreover, a fundamental result on trajectory convergence towards equilibrium points (complete stability) for reciprocal standard CNNs is extended to reciprocal FR-CNNs by using a generalized Lyapunov approach. As a consequence, it is shown that the study of the ideal case with vertical straight segments in the neuron nonlinearities is able to give a clear picture and analytic characterization of the salient features of motion, such as the sliding modes along the boundary of the hypercube defined by the hard-comparator nonlinearities. Finally, it is proved that the solutions of the ideal FR model are the uniform limit as the slope tends to infinity of the solutions of a model where the vertical segments in the nonlinearities are approximated by segments with finite slope.
Sponsorship	IEEE Circuits and Systems Society
Starting Page	1736
Ending Page	1749
Page Count	14
File Size	1008427
File Format	PDF
ISSN	15498328
Volume Number	54
Issue Number	8
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2007-08-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Cellular neural networks Neurons Neural networks Very large scale integration Stability Motion analysis Hypercubes H infinity control Linear matrix inequalities Vectors variational inequalities Cellular neural networks (CNNs) differential inclusions full-range (FR) model sliding modes trajectory convergence
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering Hardware and Architecture

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