Controlling the Primary Mirror in a Space-Based Telescope Utilizing an Eigenstructure Assignment Technique : 9781249602828 : 10 Oct 2012 : The feasibility of using a sparse array of mirrors in a satellite system is being evaluated. This study focuses on the control laws necessary for achieving the minimization of the effect of vibration which happens at the primary mirror of the satellite, by using the eigenstructure assignment technique. White Gaussian noise was assumed as the external input. AFRL has developed a 79 state model with 9 control inputs and 9 outputs, 3 sparse array mirrors, and a base. To extend the theory, a simplified model with 2 mirrors and a base which has 12 states, 4 control inputs and 8 outputs was developed. The system is not completely controllable nor observable because there are 4 rigid body modes. The control law starts from realizing the states which are controllable or uncontrollable. Then only for the controllable states, the eigenstructure assignment tec