Routh stability test is covered in almost all undergraduate control texts. It determines the stability or, a little beyond, the number of unstable roots of a polynomial in terms of the signs of certain entries of the ...Routh stability test is covered in almost all undergraduate control texts. It determines the stability or, a little 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. Keywords Routh stablity criterion - Orthonormal basis - Root-mean-squared value - Hankel operater - Nehari problem - Model reduction This work was supported by the Hong Kong Research Grants Council.展开更多
文摘Routh stability test is covered in almost all undergraduate control texts. It determines the stability or, a little 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. Keywords Routh stablity criterion - Orthonormal basis - Root-mean-squared value - Hankel operater - Nehari problem - Model reduction This work was supported by the Hong Kong Research Grants Council.
