This paper proposes a novel lifting method which converts the standard discrete-time linear periodic system to an augmented linear time-invariant system. The linear quadratic optimal control is then based on the solution of the discrete-time algebraic Riccati equation associated with the augmented linear time invariant model. An efficient algorithm for solving the Riccati equation is derived by using the special structure of the augmented linear time-invariant system. It is shown that the proposed method is very efficient, compared to the ones that use algorithms for discrete-time periodic algebraic Riccati equation. The efficiency and effectiveness of the proposed algorithm is demonstrated by the simulation test for the design problem of spacecraft attitude control using magnetic torques. Published by Elsevier Ltd.