Dissipativity and Integral Quadratic Constraints: Tailored Computational Robustness Tests for Complex Interconnections

A central notion in systems theory is dissipativity, which was 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 1960s. It provides a technique for analyzing the stability of an interconnection of some linear system in feedback with a whole class of systems, also referred to as uncertainty. This article surveys the key ideas of exploiting dissipativity and IQCs to systematically construct computational tests for robust stability and performance of uncertain interconnections in terms of linear matrix inequalities. The article focuses on the recently introduced notion of finite-horizon IQCs with a terminal cost, which is shown to provide a seamless link between dissipativity theory and absolute stability theory based on dynamic IQCs.