Stability Transfer for Autonomous Systems via Higher-Order Taylor-Truncated Lyapunov Certificates
Abstract
We develop analytical sufficient conditions for certifying the local asymptotic stability of nonlinear autonomous systems based on Lyapunov functions derived from their finite-order Taylor polynomial approximations. This approach translates the stability analysis problem from the original nonlinear dynamics to a more computationally tractable polynomial domain. The derived conditions allow for the explicit calculation of a guaranteed inner approximation of the region of attraction (ROA). We show how sum-of-squares (SOS) programming and grid search can be used to systematically search for polynomial Lyapunov functions that yield a large certified threshold radius and extract a certified invariant set inner approximation of the ROA of the nonpolynomial original system. The framework is then applied to a control tuning problem: finding reduced-effort Linear Quadratic Regulator (LQR) controllers that ensure that a given initial state of interest belongs to the certified ROA of the nonpolynomial closed loop system. The effectiveness of the overall methodology is demonstrated using a pendulum with nonlinear damping and a nonlinear control system.
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BibTeX
@misc{hoyos2026stability,
title = {{Stability Transfer for Autonomous Systems via Higher-Order Taylor-Truncated Lyapunov Certificates}},
author = {Jose D. Hoyos and Zehui Lu and Shaoshuai Mou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17604},
eprint = {2610.17604},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17604},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stability Transfer for Autonomous Systems via Higher-Order Taylor-Truncated Lyapunov Certificates
AU - Jose D. Hoyos
AU - Zehui Lu
AU - Shaoshuai Mou
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17604
UR - https://arxiv.org/abs/2610.17604
AB - We develop analytical sufficient conditions for certifying the local asymptotic stability of nonlinear autonomous systems based on Lyapunov functions derived from their finite-order Taylor polynomial approximations. This approach translates the stability analysis problem from the original nonlinear dynamics to a more computationally tractable polynomial domain. The derived conditions allow for the explicit calculation of a guaranteed inner approximation of the region of attraction (ROA). We show how sum-of-squares (SOS) programming and grid search can be used to systematically search for polynomial Lyapunov functions that yield a large certified threshold radius and extract a certified invariant set inner approximation of the ROA of the nonpolynomial original system. The framework is then applied to a control tuning problem: finding reduced-effort Linear Quadratic Regulator (LQR) controllers that ensure that a given initial state of interest belongs to the certified ROA of the nonpolynomial closed loop system. The effectiveness of the overall methodology is demonstrated using a pendulum with nonlinear damping and a nonlinear control system.
ER -