  A central notion in systems theory is dissipativity, which has been
introduced by Jan Willems with the explicit goal of arriving at a fundamental
understanding of the stability properties of feedback interconnections. In
robust control, the framework of integral quadratic constraints (IQCs) builds
on the seminal contributions of Yakubovich and Zames in the 1960's. It provides
a technique for analyzing the stability of an interconnection of some linear
system in feedback with a whole class of systems, also refereed to as
uncertainty.
  In this paper we survey the key ideas of exploiting dissipativity and
integral quadratic constraints for the computational analysis of robust
stability and performance properties of uncertain interconnections in terms of
linear matrix inequalities. In particular for dynamic supply rates, the paper
revolves around the notion of finite-horizon integral quadratic constraints
with a terminal cost. We reveal that this provides a seamless link between the
general IQC theorem and dissipativity theory that has been established only
rather recently.
