Stability and performance analysis on Sobolev spaces

This paper focusses on stability and performance analysis of feedback interconnections involving a linear time invariant and an uncertain system subject to some external disturbances. We extend the framework of integral quadratic constraints to general signal spaces and specifically apply this concept to Sobolev spaces. Our new framework offers the possibility for a natural generalization from constraints on the inputs and outputs of uncertainties to relations among derivatives thereof. In addition, it allows to impose performance criteria that put special emphasis on chosen derivatives.