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In this note, we propose a generalized stabilizing receding horizon control scheme for input/state constrained linear discrete time-varying systems that improves feasibility and on-line computation on the constrained finite-horizon optimization problem, compared with existing schemes. The control scheme is based on a time-varying horizon cost function with time-varying terminal weighting matrices, which can easily be implemented via linear matrix inequality technique. We discuss modifications of the proposed scheme that improve feasibility or on-line computation time. Through simulation examples, we illustrate the results of these schemes.