Path-connectedness of frequency-domain uncertainty sets in the graph topology

Abstract

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. © 2011 IFAC.