Application of Dixon resultant to satellite trajectory control by pole placement

Control system design process based on pole placement frequently requires to solve underdetermined multivariate polynomial systems. Since only the real solutions can be accepted for hardware implementation, we are looking for exclusively these roots. In this present study a symbolic–numeric approach is introduced to determine directly the real solutions. Employing Dixon resultant, a condition can be formulated for the free variables as parameters of the underdetermined system, which ensures only real solutions. Numerical examples illustrate the procedure and the effectiveness of the designed control.