Robust stability of diagonally dominant systems

Sufficient conditions for the stability of diagonally dominant systems subject to perturbation are developed using a theorem of Varah. The computation of perturbation bounds is simplified by use of L1 and L¿¿ norms. These yield Nyquist type graphical interpretation. It is shown that if the perturbations are `diagonal¿¿, then the norm bounds can be improved by the use of optimal similarity transformations, or equivalently optimal `generalised¿¿ dominance measures, on the nominal system return difference matrix.