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This paper deals with the problem of reducing the online computational complexity of receding horizon control (RHC) algorithms for a class of linear systems with a polytopic system description and with bounded additive disturbances. We explore a class of admissible polytopic controller dynamics involving a disturbance feedforward term for a dynamic policy which ensures reduced conservativeness and also offers a way to significantly simplify the online computations by allowing the controller dynamics to be optimized offline. Moreover, for a deterministically time-varying system with additive disturbances, we explore the use of the proposed dynamic policy as the terminal control policy appended to a standard finite-horizon disturbance-based RHC policy. We also present results on the stability of the system under the RHC schemes based on the proposed policy, in the context of both the nominal and the (H∞-based) minmax cost minimizations. Results of simulation studies that illustrate the effective performance and the computational efficiency of the proposed control schemes are included.