Relation between some criteria for the stability of constant linear multivariable systems

The paper establishes the nature of the time function (which turns out to be a distribution) that corresponds to a Laplace transform that is bounded and holomorphic in a half plane. This relationship is used to generalise the contraction-mapping stability criterion for constant linear multivariable systems. It is shown that the generalisation, which has the same frequency response interpretation as Rosenbrock´s diagonal-dominance criterion, includes the cases considered earlier by Desoer and Wu (`Stability of multiple-loop feedback linear time invariant systems¿, J. Maths. Anal. & Appl., 1968, 23, pp. 121¿129) and Rosenbrock [`Design of multivariable control systems using the inverse Nyquist array¿, Proc. IEE, 1969, 116, (11), pp. 1929¿1936] as particular cases.