Singular-value-decomposition approach to multivariable generalised predictive control

A change of basis, from the standard set to the set of eigenvectors, provides the means for the decomposition of a multivariable problem into a set of scalar problems. This idea was deployed in an earlier paper to embed scalar generalised predictive control into the multivariable framework. Eigen-decompositions, however, can be sensitive to perturbations and cannot be applied to nonsquare matrices. The paper shows how an analogous approach to multivariable predictive control can be based on a singular-value decomposition, and illustrates its applicability to nonsquare systems as well as demonstrates its superior sensitivity properties by means of two numerical examples.