New table to implement Routh´s stability test and matrix continued fraction expansion and inversion

A new table of numbers, obtained by rearranging the well known Routh stability array, is used to perform Routh´s stability test. The proposed table, with slight modifications, can also be used to expand a known rational transfer function matrix into one of the three Cauer-form continued fractions, or, conversely, to invert a given Cauer-form continued fraction. In all the aforementioned applications, the recursive relations presented for the construction of the proposed table seem better than the relevant Routh-type relations, as one may follow more easily the values of the indices appearing in the formulas, while the number of the variables involved is significantly decreased. Moreover, from the programming point of view, they guarantee a reduction of the required memory, nearly by half, and a faster execution of the corresponding program. These advantages are achieved without increase of the number of numerical operations or in the complexity of the existing techniques.