Abstract: The stability of the linear periodic system is determined by it's characteristic exponent. This paper studies how to assign characteristic exponent for linear periodic system. In order to do this, the original system has to be converted to the block controllable form by rotating transform first. Then based on the block controllable form, a method to design a periodic state feedback control law is presented, which can arbitrarily relocate the system's characteristic exponents. A sufficient condition that characteristic exponent can be assigned arbitrarily for linear periodic system is also attained in the paper. The method has been applied to controller design of small satellite using magnetorquer. The simulation result demonstrates the validity of this method to control the 1inear periodic system.