Stability analysis with integral quadratic constraints: A dissipativity based proof

In this paper we formulate a dissipativity based proof of the well-known integral quadratic constraint (IQC) theorem under mild assumptions. For general dynamic (frequency dependent) IQC-multipliers it is shown that, once the conditions of the IQC-theorem are satisfied, it is possible to construct a nonnegative Lyapunov function that satisfies a dissipation inequality. This not only shows that IQCs can be interpreted as dynamic supply functions, but also opens the way to merge frequency-domain techniques with time-domain conditions known from Lyapunov-theory.