  In this paper we provide a complete link between dissipation theory and a
celebrated result on stability analysis with integral quadratic constraints.
This is achieved with a new stability characterization for feedback
interconnections based on the notion of finite-horizon integral quadratic
constraints with a terminal cost. As the main benefit, this opens up
opportunities for guaranteeing constraints on the transient responses of
trajectories in feedback loops within absolute stability theory. For parametric
robustness, we show how to generate tight robustly invariant ellipsoids on the
basis of a classical frequency-domain stability test, with illustrations by a
numerical example.
