Tensor SVD and distributed control

The (approximate) diagonalization of symmetric matrices has been studied in the past in the context of distributed control of an array of collocated smart actuators and sensors. For distributed control using a two dimensional array of actuators and sensors, it is more natural to describe the system transfer function as a complex tensor rather than a complex matrix. In this paper, we study the problem of approximately diagonalizing a transfer function tensor for a locally spatially invariant system, and study its application along with the technique of recursive orthogonal transforms to achieve distributed control for a smart structure.