Almost-Everywhere Stability of Systems with a Piecewise-C2 Lipschitz Continuous Vector Field
Almost-Everywhere Stability of Systems with a Piecewise-C2 Lipschitz Continuous Vector Field
复制标题
具有分段 C2 Lipschitz 连续矢量场的系统的几乎处处稳定性
DOI：
10.3182/20110828-6-it-1002.00499
复制
发表时间：
2011
期刊：
影响因子：
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通讯作者：
I. Masubuchi
中科院分区：
文献类型：
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作者：
I. Masubuchi
摘要本文利用密度函数对一类具有Lipschitz连续和分段二次可微向量场的非线性系统的几乎处处稳定性进行了分析。证明AES的一个关键结果是用密度函数定义的测度的单调性，从而得出任何非收敛初值的子集都有零勒贝格测度。通过对密度函数在集合上的积分进行变量变换，证明了其单调性。这种沿轨迹的变量变化对于不可连续可微的向量场是不可用的，即使它们在状态空间的几乎所有点上都是光滑的。本文给出了证明测度单调性的另一个不等式。在此不等式的基础上，给出了具有Lipschitz连续和分段二次可微向量场的系统AES的一个保证准则。这使我们能够将密度函数的方法应用于更广泛的系统。版权所有©2011 IFAC
Abstract This paper considers analysis of almost-everywhere stability (AES) of a class of nonlinear systems that have a Lipschitz continuous and piecewise twice differentiable vector field by using density functions, which were first proposed for systems with a continuously differentiable vector field. A key result to prove AES was monotonicity of a measure defined with a density function to conclude that any subset of non-convergent initial values has zero Lebesgue measure. The monotonicity is proved via change-of-variables in integrals of the density function over a set. Such a change-of-variables along trajectories is not available for vector fields that are not continuously differentiable, even though they are smooth at almost all points of the state space. In this paper, an alternative inequality is presented that proves monotonicity of a measure. Based on this inequality, we provide a criterion to guarantee AES of systems with a Lipschitz continuous and piecewise twice differentiable vector field. This allows us to apply methods of density functions to a wider class of systems. Copyright © 2011 IFAC
表征正不变性和区域几乎吸引力的密度函数及其相反结果
DOI：
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发表时间：
2006
期刊：
Proceedings of the 45th IEEE Conference on Decision and Control
影响因子：
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作者：
平野雄大;飯島大輔;青木優介;嶋野慶次;I.Masubuchi;I.Masubuchi;増淵 泉;増淵 泉;M.Yamashita;I.Masubuchi;増淵 泉;I.Masubuchi;I.Masubuchi;I.Masubuchi
通讯作者：
I.Masubuchi
通过具有相反结果的密度函数分析正不变性和近似区域吸引力
DOI：
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发表时间：
2007
期刊：
IEEE Transactions on Automatic Control 52・7(掲載決定)
影响因子：
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作者：
平野雄大;飯島大輔;青木優介;嶋野慶次;I.Masubuchi;I.Masubuchi
通讯作者：
I.Masubuchi