Comments on "Reduced conservatism in stability robustness bounds by state transformation" [with reply]

Reference is made to the paper by R.K. Yedavalli and Z. Liang (see ibid., vol.AC-31, p.863-6, 1986) in which it is shown that state transformation can reduce the conservatism in stability robustness bounds. An attempt is made by the commenters to prove that for unstructured perturbations there always exists a better bound than that reported in the above paper, which can be obtained without using state transformations. In replying, the original authors point out that the result given by the commenters is useful in the sense that it provides the ´best´ answer as far as unstructured perturbations are concerned. However, there exist some limitations. They claim that, as far as Lyapunov-based time domain methods are concerned, the question of finding the ´best´ transformation, either for unstructured or structured, time-varying perturbations is still an open problem.<>