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This technical note elaborates on the flexibility of an approach that combines \nu-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 \nu-gap ball robust stability result can be recovered within the blended IQC/\nu-gap framework, which only requires the existence of \nu-gap continuous paths within the uncertainty set of interest. This is achieved, in part, by showing that sufficiently small \nu-gap balls are pathwise connected in the graph topology. A linear fractional characterisation of the \nu-gap is a key ingredient. This characterisation is underpinned by a certain J-spectral factorisation, also shown to exist herein. [ABSTRACT FROM AUTHOR]

A framework is established for directly accommodating feedback interconnections of unstable distributed-parameter transfer functions in robust stability analysis via integral quadratic constraints (IQCs). This involves transfer function homotopies that are continuous in a \nu-gap metric sense. As such, the development includes the extension of \nu-gap metric concepts to an irrational setting and the study of uncertainty-set connectedness in these terms. The main IQC based robust stability result is established for constantly-proper transfer functions in the Callier-Desoer algebra; i.e. finitely many unstable poles and a constant limit at infinity. Problems of structured robust stability analysis and robust performance analysis are considered to illustrate use of the main result. Several numerical examples are also presented. These include stability analysis of an autonomous system with uncertain time-delay and a closed-loop control system, accounting for both the gain and phase characteristics of the distributed-parameter uncertainty associated with the nominal rational plant model used for controller synthesis. [ABSTRACT FROM AUTHOR]