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The control of flexible mechanical systems has been extensively studied in a variety of fields. For mechanical systems with collocated sensors and actuators, the use of symmetric controllers is known to be effective. The symmetric controller guarantees the robust stability of the closed-loop system irrespective of the system parameters by virtue of the structure of the dynamical equation having positive definite or semidefinite symmetric coefficient matrices. Although this controller is superior to existing parametric approaches, systematic procedures for obtaining specific control performance other than the stability of the closed-loop system have not yet been fully established. This paper proposes an optimal design method for symmetric controllers in the sense of the H infin norm by solving the linear matrix inequalities reduced from the bounded real lemma under the symmetry constraint. This method is then extended to static output feedback control and gain-scheduled control. Finally, the design method is applied to a flexible spacecraft attitude control problem, and its validity is confirmed.