Separable Lyapunov functions for monotone systems
Separable Lyapunov functions for monotone systems
复制标题
单调系统的可分离李亚普诺夫函数
DOI：
10.1109/cdc.2013.6760604
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
G. Dirr
中科院分区：
文献类型：
--
作者：
A. Rantzer;Björn S. Rüffer;G. Dirr
可分离李雅普诺夫函数在大系统稳定性分析中起着至关重要的作用。如果一个李雅普诺夫函数可以分解成具有一维参数的函数的最大值，那么它就被称为最大可分函数。同样，如果它是这些函数的和，则称为可分离和。本文证明了紧态空间上单调系统的渐近稳定性意味着极大可分Lyapunov函数的存在性。在非紧态空间上构造了两个不存在极大可分Lyapunov函数的系统。其中一个有一个和可分李雅普诺夫函数。另一个则不然。
Separable Lyapunov functions play vital roles, for example, in stability analysis of large-scale systems. A Lyapunov function is called max-separable if it can be decomposed into a maximum of functions with one-dimensional arguments. Similarly, it is called sum-separable if it is a sum of such functions. In this paper it is shown that for a monotone system on a compact state space, asymptotic stability implies existence of a max-separable Lyapunov function. We also construct two systems on a non-compact state space, for which a max-separable Lyapunov function does not exist. One of them has a sum-separable Lyapunov function. The other does not.