Polynomial Lyapunov Functions for Exponential Stability of Nonlinear Systems on Bounded Regions
Polynomial Lyapunov Functions for Exponential Stability of Nonlinear Systems on Bounded Regions
复制标题
有界区域上非线性系统指数稳定性的多项式 Lyapunov 函数
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
P. Bliman
中科院分区：
文献类型：
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作者：
M. Peet;P. Bliman
摘要本文证明了用多项式Lyapunov函数研究非线性常微分方程在有界区域上的指数稳定性是不保守的。主要结果表明，如果存在一个n次连续可微的Lyapunov函数证明了在一个有界的子集上的指数衰减，那么就存在一个多项式Lyapunov函数证明了在同一区域上的相同衰减速率。我们的研究的动机是使用半定规划来构造多项式李雅普诺夫函数的延迟和非线性微分方程系统。
Abstract This paper presents a proof that the use of polynomial Lyapunov functions is not conservative for studying exponential stability properties of nonlinear ordinary differential equations on bounded regions. The main result implies that if there exists an n-times continuously differentiable Lyapunov function which proves exponential decay on a bounded subset of ℝ n , then there exists a polynomial Lyapunov function which proves that same rate of decay on the same region. Our investigation is motivated by the use of semidefinite programming to construct polynomial Lyapunov functions for delayed and nonlinear systems of differential equations.