Analysis and Design of a $k$ -Winners-Take-All Model With a Single State Variable and the Heaviside Step Activation Function

This paper presents a
k
-winners-take-all (
k
WTA) neural network with a single state variable and a hard-limiting activation function. First, following several
k
WTA problem formulations, related existing
k
WTA networks are reviewed. Then, the
k
WTA 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 a discrete-time version of the
k
WTA model are discussed. Furthermore, two selected applications to parallel sorting and rank-order filtering based on the
k
WTA model are discussed. Finally, simulation results show the effectiveness and performance of the
k
WTA model.