Shih-Chi Liao

Shih-Chi Liao

Ph.D. student at University of Michigan, Ann Arbor.

Quadratic Constraints for Local Stability Analysis of Quadratic Systems

Authors: Shih-Chi Liao, Maziar S. Hemati, Peter Seiler

Published in 2022 IEEE 61st Conference on Decision and Control (CDC), 2022

[Paper on IEEE] / [Paper on arXiv] / [GitHub] / [Slides] / [Poster]

Abstract

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.

ValleyQC_ImageSummary

@inproceedings{liao2022quadratic,
  title={Quadratic constraints for local stability analysis of quadratic systems},
  author={Liao, Shih-Chi and Hemati, Maziar S and Seiler, Peter},
  booktitle={2022 IEEE 61st Conference on Decision and Control (CDC)},
  pages={7053--7058},
  year={2022},
  organization={IEEE},
  doi={10.1109/CDC51059.2022.9992343}
}