Methods for Computing the SVD Rank-One Approximation in a Feedback Loop

This paper examines methods to calculate a rank-one approximation using the SVD within a feedback control loop. The rank-one approximation obtained permits the control of mxn subsystems using m+n inputs. The feedback loop presents opportunities to speed up the calculation of this approximation by using information from the previous sample time. This paper will explain some modifications to the Power Method and Jacobi Method, as well as demonstrate and discuss the pros and cons of the various techniques.