Improvements to numerical testability evaluation

Abstract
In this paper, some recent theoretical developments are reviewed and associated algorithms are proposed to determine the numerical testability for large multiinput multioutput systems. In our approach, the modified nodal analysis and the usual techniques for the sensitivity computation in the frequency domain are employed. According to the theoretical basis provided by Sen and Saeks [1] the testability evaluation is related to the computation of the number of linearly independent columns in a convenient form of the sensitivity matrix with rational entries having a common denominator. Then, by extending some results already obtained in [3], it is shown that the above-mentioned number can be determined by computing the numerical rank of a matrix comprised of the coefficients obtained by expanding the numerators of the sensitivities in a suitable orthogonal polynomial series. The numerical rank computation is simplified, particularly for large systems, through an algorithm based on the estimation of the polynomial degrees, which is performed by the iterative comparison between the Chebycheff and the corresponding Stirling coefficients.

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