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Artificial neural networks (ANNs) can be used as intelligent controllers to control nonlinear, dynamic systems through learning, which can easily accommodate the nonlinearities and time dependencies. However, they require long training time and large numbers of neurons to deal with complex problems. To overcome these drawbacks, a generalised neuron (GN) has been developed that requires much smaller training data and shorter training time. Taking benefit of these characteristics of the GN, a new generalised neuron-based adaptive power system stabiliser (GNPSS) is proposed. The GNPSS consists of a GN as an identifier, which tracks the dynamics of the plant, and a GN as a controller to damp low-frequency oscillations. Results show that the proposed adaptive GNPSS can provide a consistently good dynamic performance of the system over a wide range of operating conditions.