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This paper deals with the control problem of linear stabilizable systems under linear symmetrical input constraints using output feedback control law. The basic idea consists of extending the problem to the case of static output feedback, the partial eigenstructure assignment used in the case of full-state feedback invariant controllers. A static output feedback is realized when the number of unstable eigenvalues of the open-loop system is less than the number of outputs. The methodology allows one to determine some suitable positively invariant sets of admissible initial states. An application illustrates the results.