Path-connectedness with respect to the topology induced by the ν-gap metric underpins a recent robustness result for uncertain feedback interconnections of transfer functions in the Callier-Desoer algebra; i.e. possibly distributed-parameter with only finitely many unstable poles. In this paper, we establish path-connectedness of the following uncertainty sets of such transfer functions: diagonally structured sets with path-connected entries; arbitrarily large H∞- norm balls; and suficiently small ν-gap metric balls. Proof of the latter relies on the existence of a certain J-spectral factorisation, which is also established herein.
|Original language||English (US)|
|Title of host publication||Proceedings of the 18th IFAC World Congress|
|Number of pages||6|
|Edition||1 PART 1|
|State||Published - 2011|
|Name||IFAC Proceedings Volumes (IFAC-PapersOnline)|
|Number||1 PART 1|
Bibliographical noteFunding Information:
★This work was supported in part by the Australian Research Council (DP0880494).
- Distributed-parameter uncertainty
- ν-gap metric