What can routh table offer in addition to stability?

Key words:  Routh stablity criterion  Orthonormal basis  Root-mean-squared value  Hankel operater  Nehari problem  Model reduction

摘要:

Abstract:

Routh stability test is covered in almost all undergraduate control texts. It determines the stability or, a litde beyond , the number of unstable roots of a polynomial in terms of the signs of certain entries of the Routh table constructed from the coefficients of the polynomial. The use of the Routh table, as far 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 norm, the Hankel singular values and singular vectors, model reduction, H∞ optimization, etc.