Input and output scaling and reordering for diagonal dominance and block diagonal dominance

The scaling of the input and output units has very significant effects for multivariable systems. It affects interaction, design aims, weighting functions, model order reduction, etc. The paper presents a scaling algorithm to balance the input and output units of square systems. This algorithm is independent of the order of the inputs and outputs and ensures that the row and column dominances are balanced for any choice of input-output pairs, maximises the geometric mean of the column dominance ratios. A second algorithm is then used to reorder the inputs and outputs to help obtain diagonal dominance. A third algorithm is used to obtain block diagonal dominance in large-scale systems enabling the use of simpler control structures. These algorithms can be used for dynamic multivariable system control, and can also be used for large scale systems, to divide them into sets of multivariable systems