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Spacecraft attitude control using only magnetic torques is a periodictime-varying system as the Earth magnetic field in the spacecraft body framechanges periodically while the spacecraft circles around the Earth. The optimalcontroller design therefore involves the solutions of the periodic Riccatidifferential or algebraic equations. This paper proposes an efficient algorithmfor the periodic discrete-time Riccati equation arising from a linear periodictime-varying system $(\A,\B)$, which explores and utilizes the fact that $\A$is time-invariant and only $\B$ is time-varying in the system, a specialproperties associated with the problem of spacecraft attitude control usingonly magnetic torques.

An Efficient Algorithm for Periodic Riccati Equation for Spacecraft Attitude Control Using Magnetic Torques