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.

DI MARCO, M., Forti, M., Grazzini, M., Pancioni, L. (2009). Extended LaSalle's invariance principle for full-range cellular neural networks. EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING [10.1155/2009/730968].

Extended LaSalle's invariance principle for full-range cellular neural networks

DI MARCO, MAURO;FORTI, MAURO;GRAZZINI, MASSIMO;PANCIONI, LUCA
2009-01-01

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.
2009
DI MARCO, M., Forti, M., Grazzini, M., Pancioni, L. (2009). Extended LaSalle's invariance principle for full-range cellular neural networks. EURASIP JOURNAL ON ADVANCES IN SIGNAL PROCESSING [10.1155/2009/730968].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/23313
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