frame_align

This implements the frame alignment algorithm, ALIGN, which finds a real approximation to a complex matrix.

Implements the ALIGN algorithm described in ref[1] which finds the nearest real-matrix approximation to a complex matrix. The nearest real matrix is defined as the real matrix that preserves the most orthogonality in directions with the input complex matrix, see ref[1] for details.

This algorithm is commonly used in multivariable control to find vector directions for a controller that decouple effectively. For example, there are several references to this algorithm in the control examples of ref[2].

ref [1] - J. Edmunds and B. Kouvaritakis, "Extensions of the frame alignment technique and their use in the characteristic locus design method", 1974.

ref [2] - S. Skogestad and I. Postlethwaite, "Multivariable Feedback Control, Analysis and Design", 2001.