Stability of linear constant multivariable systems

Linear multivariable systems are considered for which the elements of the plant and compensation transfer-function matrices are holomorphic functions in the right halfplane. By phrasing the problem in a functional-analytic setting, a stability criterion is developed which is a generalisation of Nyquist´s criterion and Rosenbrock´s diagonal-dominance stability criterion. The new criterion is applicable to systems with certain distributed elements, and has the same frequency-response interpretations as those of Rosenbrock´s method. The approach also leads to an error measure for the errors arising in the closed-loop frequency response when this is calculated on the basis of an approximate open-loop transfer-function matrix.