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Open Access

Extended LaSalle's Invariance Principle for Full-Range Cellular Neural Networks

  • Mauro Di Marco1Email author,
  • Mauro Forti1,
  • Massimo Grazzini1 and
  • Luca Pancioni1
EURASIP Journal on Advances in Signal Processing20092009:730968

Received: 15 September 2008

Accepted: 20 February 2009

Published: 25 March 2009


In several relevant applications to the solution of signal processing tasks in real time, a cellular neural network (CNN) is required to be convergent, that is, each solution should tend toward some equilibrium point. The paper develops a Lyapunov method, which is based on a generalized version of LaSalle's invariance principle, for studying convergence and stability of the differential inclusions modeling the dynamics of the full-range (FR) model of CNNs. The applicability of the method is demonstrated by obtaining a rigorous proof of convergence for symmetric FR-CNNs. The proof, which is a direct consequence of the fact that a symmetric FR-CNN admits a strict Lyapunov function, is much more simple than the corresponding proof of convergence for symmetric standard CNNs.


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Authors’ Affiliations

Department of Information Engineering, University of Siena, Siena, Italy


© Mauro Di Marco et al. 2009

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.