In problems of active vibration control of elastic structures, it is known that systems with symmetric feedback matrices (realized using colocated dual sensor/actuator pairs) possess many desirable properties, including real eigenvalues, infinite gain margin, no flutter instability, and the lower-bound character of Rayleigh estimation formulas. In this paper, we consider systems with nonsymmetric feedback matrices which may be transformed, via a similarity transformation, into symmetric systems. We propose constructive conditions to recognize a-priori which systems are symmetrizable. It is shown that lumped-mass structures are not symmetrizable. The results are applied in an example showing how to place sensors and actuators on a structure in such locations that the system remains symmetrizable.

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