Quadratic Constraints for Local Stability Analysis of Quadratic Systems
Dynamical Systems
2022-09-09 v1 Systems and Control
Systems and Control
Optimization and Control
Abstract
This paper proposes new quadratic constraints (QCs) to bound a quadratic polynomial. Such QCs can be used in dissipation ineqaulities 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.
Keywords
Cite
@article{arxiv.2209.03565,
title = {Quadratic Constraints for Local Stability Analysis of Quadratic Systems},
author = {Shih-Chi Liao and Maziar S. Hemati and Peter Seiler},
journal= {arXiv preprint arXiv:2209.03565},
year = {2022}
}
Comments
6 pages, 4 figures, to be published in IEEE Conference on Decision and Control 2022