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In this paper, we present a novel algorithm for implementing linear time invariant controllers in computationally constrained environments. The algorithm transforms a linear time invariant controller into a periodically time varying system, which is shown to be implemented in a computationally efficient manner. This is achieved by first decomposing the controller into a dual rate system. A scheduling policy is then adopted that interlaces the computation associated with the two systems. The interlaced dual rate implementation of the controller algorithm significantly reduces the computational overhead at each time step. A theoretical framework is developed to analyze the effect of this model of computation on the closed-loop stability performance. The paper concludes with an example based on a flight control algorithm designed for the Boeing 737-100 transport system research vehicle (TSRV) linear longitudinal motion model.