On the Symmetrizability of Structural Control Systems With Noncolocated Sensors and Actuators

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.