System analysis via integral quadratic constraints

TLDR

The approach originates from Yakubovich (1967) and has been shaped by both Western and Russian control theory traditions. The paper introduces a unified robustness analysis framework addressing nonlinearities, time variations, and uncertain parameters. It describes how complex systems can be modeled with integral quadratic constraints for their components, presents a systematic computational method, relates it to other stability techniques, and provides a comprehensive list of IQCs for key component types. A stability theorem for IQC‑described systems is presented, extending classical passivity/dissipativity results while simplifying multiplier use and causality handling.

Abstract

This paper introduces a unified approach to robustness analysis with respect to nonlinearities, time variations, and uncertain parameters. From an original idea by Yakubovich (1967), the approach has been developed under a combination of influences from the Western and Russian traditions of control theory. It is shown how a complex system can be described, using integral quadratic constraints (IQC) for its elementary components. A stability theorem for systems described by IQCs is presented that covers classical passivity/dissipativity arguments but simplifies the use of multipliers and the treatment of causality. A systematic computational approach is described, and relations to other methods of stability analysis are discussed. Last, but not least, the paper contains a summarizing list of IQCs for important types of system components.