论文标题
存在部分二次lyapunov函数，可以证明非线性系统的局部渐近稳定性
Existence of Partially Quadratic Lyapunov Functions That Can Certify The Local Asymptotic Stability of Nonlinear Systems
论文作者
论文摘要
本文提出了一种通过使用使用方案总和（SOS）编程来搜索部分二次二次lyapunov函数（LF）的方法，以证明给定非线性普通微分方程（ODE）的局部渐近稳定性。所提出的方法特别适合于具有高维状态空间的ODE的稳定性分析。这是由于与一般SOS LF相比，部分二次LF被较少的决策变量参数化。本文的主要贡献是使用中心歧管定理表明，在某些条件下存在证明给定ODE的局部渐近稳定性的部分二次LFS。
This paper proposes a method for certifying the local asymptotic stability of a given nonlinear Ordinary Differential Equation (ODE) by using Sum-of-Squares (SOS) programming to search for a partially quadratic Lyapunov Function (LF). The proposed method is particularly well suited to the stability analysis of ODEs with high dimensional state spaces. This is due to the fact that partially quadratic LFs are parametrized by fewer decision variables when compared with general SOS LFs. The main contribution of this paper is using the Center Manifold Theorem to show that partially quadratic LFs that certify the local asymptotic stability of a given ODE exist under certain conditions.
