A parametrization for automatic loop-by-loop multivariable controller design

Linear multivariable controller design is performed iteratively one column at a time via a new result which gives a parametrization of the class of all stabilizing columns when all but one of the controller columns are fixed, for a stable, strictly proper plant. All closed loop transfer matrices of interest are expressed as affine functions of a free (stable) design parameter. A dual parametrization is developed for the controller rows and the two parametrizations combined to yield a corresponding result for individual elements of the controller matrix. A systematic means of designing diagonal controllers is on important consequence.