Robustness analysis with parameter-varying integral quadratic constraints

The paper considers the analysis of the worst-case input/output gain of an interconnection of a known linear parameter varying system and a perturbation. The input/output behavior of the perturbation is described by an integral quadratic constraint (IQC). Recent results have shown that under certain technical conditions IQCs can be formulated as a finite horizon time domain constraint. The worst-case input/output gain of the interconnection can then be bounded using a dissipation inequality that incorporates the IQCs. Unlike the classical frequency domain approach to IQCs, this time domain interpretation opens up a new class of IQCs, where the IQC itself is parameter-varying. Various examples for parameter-varying IQCs for different classes of perturbations are given. A simple numerical example shows that the introduction of parameter-varying IQCs can lead to less conservative bounds on the worst-case gain.