Diagonal dominance and the method of pseudodiagonalisation

Very little practical guidance has been forthcoming on achieving a diagonally-dominant system prior to controller design, using either the Nyquist or inverse-Nyquist multivariable design techniques. In this reappraisal of pseudodiagonalisation and diagonal dominance, a linear space setting is used as a framework for the existing technique of Rosenbrock and several new related optimisations. The relationship between pseudodiagonalisation and dominance at one given frequency is discussed. In particular, sufficient conditions, for successive iterates of a pseudodiagonalisation procedure, to create dominance at that frequency are given. The extension of pseudodiagonalisation to try and create diagonal dominance per se is examined in some detail. The new technique for pseudodiagonalisation is utilised in a least-squares approach to diagonal dominance, and the new algorithm demonstrated on the example of Hawkins.