The set of stable switching sequences for discrete-time linear switched systems☆
The set of stable switching sequences for discrete-time linear switched systems☆
复制标题
DOI：
10.1016/j.jmaa.2010.11.053
复制
发表时间：
2011-05
影响因子：
1.3
通讯作者：
Yu Huang;J. Luo;Tingwen Huang;Mingqing Xiao
中科院分区：
文献类型：
--
作者：
Yu Huang;J. Luo;Tingwen Huang;Mingqing Xiao
在本文中，我们研究了离散时间切换线性系统的渐近稳定性的表征。我们首先将系统动力学转化为符号拓扑框架下的符号环境。然后利用遍历测度理论，得到渐近稳定序列集合Hausdorff维数的下界估计。我们证明，当且仅当相应的切换线性系统具有至少一个渐近稳定切换序列时，渐近稳定切换序列集合的豪斯多夫维数为正。所得结果揭示了一个潜在的基本原理：只要切换是任意的，切换线性系统要么拥有不可数的渐近稳定切换序列，要么不具有任何渐近稳定切换序列。我们还开发了频率和密度指数来识别系统的渐近稳定切换序列。
In this paper we study the characterization of the asymptotical stability for discrete-time switched linear systems. We first translate the system dynamics into a symbolic setting under the framework of symbolic topology. Then by using the ergodic measure theory, a lower bound estimate of Hausdorff dimension of the set of asymptotically stable sequences is obtained. We show that the Hausdorff dimension of the set of asymptotically stable switching sequences is positive if and only if the corresponding switched linear system has at least one asymptotically stable switching sequence. The obtained result reveals an underlying fundamental principle: a switched linear system either possesses uncountable numbers of asymptotically stable switching sequences or has none of them, provided that the switching is arbitrary. We also develop frequency and density indexes to identify those asymptotically stable switching sequences of the system.