Reconciling ν-gap metric and IQC based robust stability analysis

This technical note elaborates on the flexibility of an approach that combines ν-gap metric and integral quadratic constraint (IQC) based analysis in the study of uncertain feedback interconnections of distributed-parameter transfer functions. It is established that a standard ν -gap ball robust stability result can be recovered within the blended IQC/ν-gap framework, which only requires the existence of ν-gap continuous paths within the uncertainty set of interest. This is achieved, in part, by showing that sufficiently small ν-gap balls are pathwise connected in the graph topology. A linear fractional characterisation of the ν-gap is a key ingredient. This characterisation is underpinned by a certain J-spectral factorisation, also shown to exist herein.