%0 Journal Article
%T Extended LaSalle's Invariance Principle for Full-Range Cellular Neural Networks
%A Mauro Di Marco
%A Mauro Forti
%A Massimo Grazzini
%A Luca Pancioni
%J EURASIP Journal on Advances in Signal Processing
%D 2009
%I Springer
%R 10.1155/2009/730968
%X 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.
%U http://dx.doi.org/10.1155/2009/730968