Abstract A rather general class of neural networks, called generalized cellular neural networks (CNNs), is introduced. the new model covers most of the known neural network architectures, including cellular neural networks, Hopfield networks and multilayer perceptrons. Several sets of conditions ensuring the input‐output stability and global asymptotic stability of generalized CNNs have been obtained. the conditions for the stability of individual cells are checked in the frequency domain, while the stability of the overall network is analysed in terms of the stability of individual cells and the connectivity characteristics. the results on the global asymptotic stability are useful for the design of a generalized CNN such that the orbit of each state converges to a globally asymptotically stable equilibrium point which depends only on the input and not on the initial state. Such a network defines an algebraic map from the space of external inputs to the space of steady state values of the outputs and hence can accomplish cognitive and computational tasks.
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