Semidefinite Programming Solution to the Spacecraft Analysis and Control Problem

This paper provides a semidefinite optimization solution to the analysis and control of a rigid rotating spacecraft. Due to the quaternion representation of a rotating body, the nonlinearities that describe the system are polynomial in nature and may be expressed in the Differential Algebraic Representation (DAR). Once the system is in this form, it is possible to apply linear-based tools for the analysis and control design of the closed loop dynamics. The task is then reduced to that of a semidefinite optimization problem subject to constraints in the form of Linear Matrix Inequalities (LMIs).