Active structural acoustic radiation control of a piezolaminated arbitrary thick rectangular plate with a mixed-norm H_2/H_∞ robust controller is developed. The structure is made of a transversely isotropic host layer with a distributed piezoelectric sensor layer as well as a matched piezoelectric actuator layer, facing high frequency uncertainties and random external disturbances. The elasto-acoustic formulation, based on the exact linear 3D piezo-elasticity theory, is developed for problem of fully coupled structure and acoustic mediums. Identification of the fluid/structure interaction system with subspace algorithm is implemented on actuator/sensor data sets. A multi-objective controller with regional pole placement, formulated in LMI framework, is synthesized while unmodeled dynamics are treated as multiplicative uncertainties. Numerical simulations confirm effectiveness of the implemented multi-objective robust active control scheme for reduction of radiated acoustic power from a piezocomposite plate, without stimulating any instability. Also, better tracking performance and disturbance rejection of mixed-norm controller is observed in comparison to that of H_2 and H_∞ controllers. Finally, validity of the elasto-acoustic model is proved by results obtained from a finite element software, as well as with the data available in the literature.