Author's reply [to comments on 'On Routh-Pade model reduction of interval systems'

Abstract

The paper is reply to the article by Shih-Feng Yang (see ibid., p.273-4, 2005). Previously (Dolgin and Zeheb, 2003), it was shown that the existing generalization of the direct Routh table truncation method for interval systems fails to produce a stable system. Additionally, it was shown how to extend the method to ensure the stability of the resulting interval system. Although the main statement of Dolgin and Zeheb (2003) is correct, there is, however, an omission in the proposed algorithm of building interval Routh table:the newly calculated line in the table may be inconsistent with the last existing line. Two additional conditions should be formulated to avoid this situation. The main idea is to shrink the uncertainty of the elements of the last existing line of the table, in the procedure of building the new line.