System analysis via integral quadratic constraints

1997/06/01 by A. Megretski, Alexandre Megretski, A. Rantzer +1 · 1,516 citations
Engineering · Mathematics · #Advanced Control Systems Optimization #Applied mathematics #Causality (physics) #Computer science #Control (management) #Control and Stability of Dynamical Systems #Control theory (sociology) #Engineering #Mathematical optimization #Mathematics #Passivity #Quadratic equation #Robustness (evolution) #Stability (learning theory) #Stability and Control of Uncertain Systems

paper · doi:10.1109/9.587335

published in IEEE Transactions on Automatic Control 42(6), 819-830 (Institute of Electrical and Electronics Engineers)

openalex publication_date 1997/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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.

Citations

• Dissipative dynamical systems part I: General theory

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