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In this paper, we propose a neural network for solving a class of convex quadratic minimax problems with constraints. Four sufficient conditions are provided to ensure the asymptotic stability of the proposed network. Furthermore, the exponential stability of the proposing network is also proved under certain conditions. The results obtained here can be further extended to the globally projected dynamical system. In addition, some new stability conditions for the system are also obtained. Since our stability conditions can be easily checked in practice, these results becomes more attractive in real applications.