Stability and performance analysis of nonlinear and non-normal systems using quadratic constraints

Aniketh Kalur, Peter Seiler, Maziar S. Hemati

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations


We propose a system-theoretic approach for analyzing stability and transient energy growth performance of nonlinear fluid flow systems. The systems in consideration are composed of a non-normal linear element in feedback with a static and lossless nonlinearity—the NavierStokes equations being a special case. Specifically, we show that the input-output properties of the nonlinear element can be represented by a set of quadratic constraints. As a result, the nonlinear system can be analyzed by solving the Lyapunov inequalities of a linear system with a set of quadratic constraints that capture nonlinear behavior. Here, we investigate the proposed analysis framework on the Waleffe-Kim-Hamilton model—a low-dimensional mechanistic model of transitional and turbulent shear flows. Our proposed analysis framework can analyze global and local stability of a given equilibrium point of the nonlinear system. We show that nonlinear flow interactions have a destabilizing effect on the system response. The Lagrange multipliers in the proposed analysis provide additional information regarding the dominant nonlinear flow interaction terms.

Original languageEnglish (US)
Title of host publicationAIAA Scitech 2020 Forum
PublisherAmerican Institute of Aeronautics and Astronautics Inc, AIAA
ISBN (Print)9781624105951
StatePublished - 2020
EventAIAA Scitech Forum, 2020 - Orlando, United States
Duration: Jan 6 2020Jan 10 2020

Publication series

NameAIAA Scitech 2020 Forum
Volume1 PartF


ConferenceAIAA Scitech Forum, 2020
Country/TerritoryUnited States

Bibliographical note

Funding Information:
This material is based upon work supported by the Air Force Office of Scientific Research under award number FA9550-19-1-0034, monitored by Dr. Gregg Abate.

Publisher Copyright:
© 2020, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.

Copyright 2021 Elsevier B.V., All rights reserved.


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