  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.
