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In this technical note we study the computation of the Maximal Output Admissible Set for linear systems subject to polynomial constraints. The computation of an inner approximation of the Maximal Output Admissible Sets requires the determination of constraint redundancy. We use a procedure to determine polynomial constraint redundancy based on a consequence of Putinar's Positivstellensatz. Further, we present a modification of the algorithm to compute the Maximal Output Admissible Set with improved performance. Lastly, demonstrate the potential for practical applications in two case studies of spacecraft rendezvous and control of an electromagnetic actuator.