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This paper proposes a novel lifting method which converts the standarddiscrete-time linear periodic system to an augmented linear time-invariantsystem. The linear quadratic optimal control is then based on the solution ofthe discrete-time algebraic Riccati equation associated with the augmentedlinear time-invariant model. An efficient algorithm for solving the Riccatiequation is derived by using the special structure of the augmented lineartime-invariant system. It is shown that the proposed method is very efficientcompared to the ones that use algorithms for discrete-time periodic algebraicRiccati equation. The efficiency and effectiveness of the proposed algorithm isdemonstrated by the simulation test for the design problem of spacecraftattitude control using magnetic torques.

An Efficient LQR Design for Discrete-Time Linear Periodic System Based on a Novel Lifting Method