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

Abstract

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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Correspondence to Mauro Di Marco.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Di Marco, M., Forti, M., Grazzini, M. et al. Extended LaSalle's Invariance Principle for Full-Range Cellular Neural Networks. EURASIP J. Adv. Signal Process. 2009, 730968 (2009). https://doi.org/10.1155/2009/730968

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Keywords

  • Direct Consequence
  • Information Technology
  • Signal Processing
  • Equilibrium Point
  • Quantum Information