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Frequency domain criteria for cellular neural networks
Author(s) -
PERFETTI RENZO
Publication year - 1997
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/(sici)1097-007x(199703/04)25:2<55::aid-cta949>3.0.co;2-x
Subject(s) - cellular neural network , frequency domain , stability (learning theory) , artificial neural network , domain (mathematical analysis) , computer science , equilibrium point , exponential stability , state space , trajectory , mathematics , control theory (sociology) , point (geometry) , state (computer science) , fourier transform , discrete fourier transform (general) , algorithm , artificial intelligence , fourier analysis , mathematical analysis , machine learning , differential equation , fractional fourier transform , control (management) , statistics , physics , geometry , nonlinear system , quantum mechanics , astronomy
A dynamical system is called globally asymptotically stable if it has a unique equilibrium point which attracts every trajectory in state space. As a consequence its steady state response is insensitive to initial conditions and then depends only on the input. In this paper some criteria are presented for the global asymptotic stability of cellular neural networks (CNNs), concerning both discrete‐time and continuous‐time dynamics. The proposed criteria represent necessary and sufficient conditions that can easily be checked by computing the discrete Fourier transform of the template elements. For this reason they have been called frequency domain stability criteria. These criteria provide milder constraints on the template coefficients than required in existing results for general recurrent neural network models. © 1997 by John Wiley & Sons, Ltd.