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This paper presents a k-winners-take-all (kWTA) neural network with a single state variable and a hard-limiting activation function. First, following several kWTA problem formulations, related existing kWTA networks are reviewed. Then, the kWTA model model with a single state variable and a Heaviside step activation function is described and its global stability and finite-time convergence are proven with derived upper and lower bounds. In addition, the initial state estimation and adoi:10.1109/tnn.2010.2052631 pmid:20709640 fatcat:63joiqudnbbvnprnut6lu7hc7m