Routh stability test is covered in almost all undergraduate control texts. It detemines the stability or, a luttle beyond, the number of unstable roots of a polynomial in tems of the signs of certain entries of the Routh table constructed from the coefficients of the polynomial. The use of the Routh table, as fir as the common textbooks show, is only limited to this function.We will show that the Routh table can actually be used to construct an orthonormal basis in the space of strictly proper rational functions with a common stable denominator. This orthonormal basis can then be used for many other purposes, including the computation of the H2 nom, the Hankel singular values and singular vectors, model reduction, H∞ optimization, etc.
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