Stability analysis by dynamic dissipation inequalities: On merging frequency-domain techniques with time-domain conditions

This paper provides a complete link between dissipative systems theory and a celebrated result on stability analysis with integral quadratic constraints (IQCs). 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 systems affected by parametric uncertainties, 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.