Quadratic Constraints for Local Stability Analysis of Quadratic Systems

Shih Chi Liao, Maziar S. Hemati, Peter Seiler

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


This paper proposes new quadratic constraints (QCs) to bound a quadratic polynomial. Such QCs can be used in dissipation inequalities to analyze the stability and performance of nonlinear systems with quadratic vector fields. The proposed QCs utilize the sign-indefiniteness of certain classes of quadratic polynomials. These new QCs provide a tight bound on the quadratic terms along specific directions. This reduces the conservatism of the QC bounds as compared to the QCs in previous work. Two numerical examples of local stability analysis are provided to demonstrate the effectiveness of the proposed QCs.

Original languageEnglish (US)
Title of host publication2022 IEEE 61st Conference on Decision and Control, CDC 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781665467612
StatePublished - 2022
Event61st IEEE Conference on Decision and Control, CDC 2022 - Cancun, Mexico
Duration: Dec 6 2022Dec 9 2022

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Conference61st IEEE Conference on Decision and Control, CDC 2022

Bibliographical note

Funding Information:
*This research was sponsored by the US Army Research Office and was accomplished under Grant Number W911NF-20-1-0156. The work of Maziar S. Hemati was supported in part by the Air Force Office of Scientific Research under award numbers FA9550-21-1-0106 and FA9550-21-1-0434, the National Science Foundation under award number CBET-1943988, and the Office of Naval Research under award number N000140-22-1-2029.

Publisher Copyright:
© 2022 IEEE.


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